0132_0321_1023_2103<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 20, 60, 172, 492, 1420, 4116, 11932, 34564, 100092, 289860, 839484, 2431364, 7041852, 20394884, 59068348, 171075844, 495476284, 1435017348, 4156151996, 12037205508, 34862612284, 100970424196, 292434386364, 846959603972, 2452996652092, 7104462297732, 20576214198972, 59593614980100, 172597296679228, 499882862140804, 1447779777959868, 4193114915952388, 12144259069007420, 35172665498460292, 101868412987393212, 295035176251488772, 854492110685250364, 2474812585062671236, 7167646435346444732, 20759210508392783108, 60123615864562430012, 174132305425007552132, 504328612918644334268, 1460655730639150055428, 4230406740363069783356, 12252265070755764758916, 35485476593009135651772, 102774388389503401550596, 297659096705421910870588, 862091609007684876725380, 2496822541449046446930108, 7231392509044248143463940, 20943834314116964796028732, 60658330360103429870530436, 175680965905816180338304444, 508813902367159065715730692, 1473646196713709472521544764, 4268030222809704059727590020, 12361231633101385193277854396, 35801069699688285602344602628, 103688421161019934561002795324, 300306353219346861255838102916, 869758694115465727166325407676, 2519028245256267812377827569412, 7295705513874941269684184792636, 21130100087373278474152244672644, 61197800384527081642531358026940, 177243399530436965128878639878660, 513339082119182772099544492935996, 1486752194604080864243144754641796, 4305988312900070821296030690302396, 12471167298844695498562136939885828, 36119469560525648247385793145346108, 104610582960794371087809876377714308, 302977153334418518994363279346550460, 877493967097291232468468021821904900, 2541431437380495454920044584843863356, 7360590491888555935829115253141995908, 21318022431139385950244788212379644860, 61742068231533780918133833428439235332, 178819728791495987673811680874723373628, 517904506942524024905776287881005401220, 1499974751802300684903874531965307445436, 4344283986495729607515053289177315679748, 12582080686789251584106392583736394301244, 36440701137628241219139537073556397246340, 105540946085031474968313759281430704295356, 305671706437657751853475357193259479531780, 885298034387823488405643720999480884055100, 2564033874200887270673872732804967232588420, 7426052529977281992368507890894320378706620, 21507616078266126827012164880903026519974916, 62291176570967070812742096245417335047625020, 180410077271018737448201634641230461814345092, 522510534760150332618448901597011918880221116, 1513314904938495060413609976764142628657268484, 4382920245924320558501619819368388457050744380<br /><br />


Generating function in Maple syntax:<br />
-(2*x-1)*(x-1)^2/(4*x^5-6*x^3+8*x^2-5*x+1)<br /><br />



Generating function in latex syntax:<br />
-\frac{\left(2 x -1\right) \left(x -1\right)^{2}}{4 x^{5}-6 x^{3}+8 x^{2}-5 x +1}<br /><br />



Generating function in sympy syntax:<br />
(1 - 2*x)*(x - 1)**2/(4*x**5 - 6*x**3 + 8*x**2 - 5*x + 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(4*x^5-6*x^3+8*x^2-5*x+1)*F(x)+(2*x-1)*(x-1)^2 = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(4 x^{5}-6 x^{3}+8 x^{2}-5 x +1\right) F \! \left(x \right)+\left(2 x -1\right) \left(x -1\right)^{2} = 0<br /><br />



Explicit closed form in Maple syntax:<br />
-9687744/6713281*((((RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-71/121)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-71/121*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+607/1452)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+(-71/121*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+607/1452)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+607/1452*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-133/484)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+((-71/121*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+607/1452)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+607/1452*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-133/484)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+(607/1452*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-133/484)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-133/484*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-581/2904)*((((172/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-1)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-4343/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+1059/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+925/6672-301/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^3+((172/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-1)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^3+(-11015/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+2419/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(379/1112*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-3923/3336)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+1147/2224+925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^2+((-4343/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+1059/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^3+(379/1112*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-3923/3336)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-14667/4448+76687/13344*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)-16961/4448*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+34769/13344)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+(925/6672-301/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^3+(1147/2224+925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-16961/4448*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+34769/13344)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)-9121/4448+34769/13344*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+1)+(((4343/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-172/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2+301/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(4343/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2-119/278*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-21/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)-63/1112-21/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+301/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^2+((4343/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2-119/278*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-21/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-119/278*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2-19759/4448+93851/13344*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)-21/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2-19759/4448*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+41077/13344)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+(-63/1112-21/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+301/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-21/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2-19759/4448*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+41077/13344)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)-9121/4448-63/1112*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2+41077/13344*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+1)+(((1-172/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-85/139+RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^4+((-85/139+RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+202/139-85/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^3+((-3/2+258/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+255/278-3/2*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^2+((-1723/556+3863/834*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+1057/1668-1723/556*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+(4693/1668-2233/556*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+4693/1668*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-355/278)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+1)+(((172/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-1)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-4343/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+1059/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+925/6672-301/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^2+((-4343/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+1059/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-2177/1668+119/278*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+1273/2224+21/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+(925/6672-301/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(1273/2224+21/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+63/1112*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-1577/3336)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+2)+(((1-172/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-85/139+RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^3+((-85/139+RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+202/139-85/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^2+((-431/3336+97/1112*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+63/1112-431/3336*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+(63/1112-431/3336*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+63/1112*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-1577/3336)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+2)+(((1-172/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-85/139+RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^2+((-1059/2224+4343/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+8771/6672-1059/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+(-925/6672+301/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-1147/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+3)+(((-3345/556+3589/417*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+6733/1668-3345/556*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+(6733/1668-3345/556*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+6733/1668*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-1163/278)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+1)+(((4573/3336-1967/1112*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-957/1112+4573/3336*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+(-957/1112+4573/3336*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-957/1112*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+5695/3336)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+2)+(((301/2224-2329/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-925/6672+301/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+(-925/6672+301/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-1147/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+3)+(((-1+172/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+85/139-RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+(85/139-RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+85/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-202/139)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+4)+(((-1059/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2-925/6672)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-1059/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2+2177/1668*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-1273/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+1577/3336-1273/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^2+((-1059/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2+2177/1668*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-1273/2224)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(2177/1668*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2+39655/13344-22519/4448*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)-1273/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2+39655/13344*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-7709/4448)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+(1577/3336-1273/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-1273/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2+39655/13344*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)-7709/4448)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+18221/13344+1577/3336*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^2-7709/4448*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n)+(((85/139-RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(1059/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-8771/6672)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+1147/2224+925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^3-((RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-85/139)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(-1059/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+8771/6672)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)-1147/2224-925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^2+((1059/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-8771/6672)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^3+(1147/2224+925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^2+(58667/13344-17427/4448*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+33347/13344*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-12019/4448)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+(1147/2224+925/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^3+(33347/13344*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-12019/4448)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+9345/4448-7709/4448*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n)+(((-85/139+RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+202/139-85/139*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^4+((255/278-3/2*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-303/139+255/278*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^2+((16177/6672-7125/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)+1031/2224+16177/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)+(-4289/2224+18061/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-4289/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+6205/6672)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n)+(((24337/6672-11573/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-5433/2224+24337/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 2)+(-5433/2224+24337/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3))*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 4)-5433/2224*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 3)+17305/6672)*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n)+2591/6672*RootOf(4*_Z^5-6*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n))<br /><br />



Explicit closed form in latex syntax:<br />
-\frac{9687744 \left(\left(\left(\left(\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{71}{121}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{71 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{121}+\frac{607}{1452}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{71 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{121}+\frac{607}{1452}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{607 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1452}-\frac{133}{484}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\left(-\frac{71 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{121}+\frac{607}{1452}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{607 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1452}-\frac{133}{484}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{607 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1452}-\frac{133}{484}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{133 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{484}-\frac{581}{2904}\right) \left(\left(\left(\left(\frac{172 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{139}-1\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{4343 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}+\frac{1059}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{925}{6672}-\frac{301 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{172 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{139}-1\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{11015 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}+\frac{2419}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{379 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{1112}-\frac{3923}{3336}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1147}{2224}+\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4343 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}+\frac{1059}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{379 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{1112}-\frac{3923}{3336}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{14667}{4448}+\frac{76687 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{13344}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{16961 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{4448}+\frac{34769}{13344}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{925}{6672}-\frac{301 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{1147}{2224}+\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{16961 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{4448}+\frac{34769}{13344}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{9121}{4448}+\frac{34769 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{13344}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(\frac{4343 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{6672}-\frac{172 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{139}+\frac{301}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{4343 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{6672}-\frac{119 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{278}-\frac{21}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{63}{1112}-\frac{21 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}+\frac{301 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{4343 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{6672}-\frac{119 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{278}-\frac{21}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{119 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{278}-\frac{19759}{4448}+\frac{93851 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{13344}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{21 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2224}-\frac{19759 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{4448}+\frac{41077}{13344}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{63}{1112}-\frac{21 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}+\frac{301 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{21 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2224}-\frac{19759 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{4448}+\frac{41077}{13344}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{9121}{4448}-\frac{63 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1112}+\frac{41077 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{13344}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1-\frac{172 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{85}{139}+\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{85}{139}+\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{202}{139}-\frac{85 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{3}{2}+\frac{258 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{255}{278}-\frac{3 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1723}{556}+\frac{3863 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{834}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1057}{1668}-\frac{1723 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{556}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{4693}{1668}-\frac{2233 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{556}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{4693 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1668}-\frac{355}{278}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(\frac{172 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{139}-1\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{4343 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}+\frac{1059}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{925}{6672}-\frac{301 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4343 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}+\frac{1059}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{2177}{1668}+\frac{119 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{278}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1273}{2224}+\frac{21 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{925}{6672}-\frac{301 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{1273}{2224}+\frac{21 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{63 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{1112}-\frac{1577}{3336}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1-\frac{172 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{85}{139}+\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{85}{139}+\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{202}{139}-\frac{85 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{431}{3336}+\frac{97 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1112}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{63}{1112}-\frac{431 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{3336}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{63}{1112}-\frac{431 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{3336}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{63 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1112}-\frac{1577}{3336}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1-\frac{172 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{85}{139}+\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1059}{2224}+\frac{4343 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{8771}{6672}-\frac{1059 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{925}{6672}+\frac{301 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{6672}-\frac{1147}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{3345}{556}+\frac{3589 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{417}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{6733}{1668}-\frac{3345 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{556}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{6733}{1668}-\frac{3345 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{556}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{6733 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1668}-\frac{1163}{278}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{4573}{3336}-\frac{1967 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1112}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{957}{1112}+\frac{4573 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{3336}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{957}{1112}+\frac{4573 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{3336}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{957 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1112}+\frac{5695}{3336}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{301}{2224}-\frac{2329 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{925}{6672}+\frac{301 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{925}{6672}+\frac{301 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{6672}-\frac{1147}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1+\frac{172 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{85}{139}-\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{85}{139}-\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{85 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{139}-\frac{202}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\frac{1059 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}+\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}-\frac{925}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1059 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2224}+\frac{2177 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1668}-\frac{1273}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1577}{3336}-\frac{1273 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}-\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1059 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2224}+\frac{2177 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{1668}-\frac{1273}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{2177 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{1668}+\frac{39655}{13344}-\frac{22519 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{4448}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1273 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2224}+\frac{39655 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{13344}-\frac{7709}{4448}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{1577}{3336}-\frac{1273 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}-\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1273 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2224}+\frac{39655 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{13344}-\frac{7709}{4448}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{18221}{13344}+\frac{1577 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{3336}-\frac{7709 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{4448}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\frac{85}{139}-\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{1059 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{2224}-\frac{8771}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1147}{2224}+\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-\left(\left(\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{85}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1059 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{2224}+\frac{8771}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1147}{2224}-\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1059 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{2224}-\frac{8771}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{1147}{2224}+\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{58667}{13344}-\frac{17427 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{4448}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{33347 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{13344}-\frac{12019}{4448}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{1147}{2224}+\frac{925 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{33347 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{13344}-\frac{12019}{4448}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{9345}{4448}-\frac{7709 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{4448}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(-\frac{85}{139}+\mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{202}{139}-\frac{85 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{139}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(\frac{255}{278}-\frac{3 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{303}{139}+\frac{255 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{278}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{16177}{6672}-\frac{7125 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1031}{2224}+\frac{16177 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{4289}{2224}+\frac{18061 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{4289 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}+\frac{6205}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{24337}{6672}-\frac{11573 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{5433}{2224}+\frac{24337 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{5433}{2224}+\frac{24337 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{5433 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{2224}+\frac{17305}{6672}\right) \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}+\frac{2591 \mathit{RootOf}\left(4 \textit{\_Z}^{5}-6 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{6672}\right)}{6713281}<br /><br />



  
    Recurrence in maple format:<br />
    
      a(0) = 1<br />
    
      a(1) = 1<br />
    
      a(2) = 2<br />
    
      a(3) = 6<br />
    
      a(4) = 20<br />
    
    a(n) = 3/2*a(n+2)-2*a(n+3)+5/4*a(n+4)-1/4*a(n+5), n >= 5<br /><br />

    Recurrence in latex format:<br />
    
      a \! \left(0\right) = 1<br />
    
      a \! \left(1\right) = 1<br />
    
      a \! \left(2\right) = 2<br />
    
      a \! \left(3\right) = 6<br />
    
      a \! \left(4\right) = 20<br />
    
    a \! \left(n \right) = \frac{3 a \! \left(n +2\right)}{2}-2 a \! \left(n +3\right)+\frac{5 a \! \left(n +4\right)}{4}-\frac{a \! \left(n +5\right)}{4}, \quad n \geq 5<br /><br />
  



  Specification 1<br />
  Strategy pack name: point_placements<br />
  Tree: http://permpal.com/tree/15417/<br />
  System of equations in Maple syntax:<br />
  
    F[0,x] = F[1,x]+F[2,x]<br />
  
    F[1,x] = 1<br />
  
    F[2,x] = F[3,x]<br />
  
    F[3,x] = F[4,x]*F[5,x]<br />
  
    F[4,x] = x<br />
  
    F[5,x] = F[20,x]+F[6,x]<br />
  
    F[6,x] = F[1,x]+F[7,x]<br />
  
    F[7,x] = F[8,x]<br />
  
    F[8,x] = F[4,x]*F[9,x]<br />
  
    F[9,x] = F[10,x]+F[13,x]<br />
  
    F[10,x] = F[1,x]+F[11,x]<br />
  
    F[11,x] = F[12,x]<br />
  
    F[12,x] = F[10,x]*F[4,x]<br />
  
    F[13,x] = F[11,x]+F[14,x]<br />
  
    F[14,x] = F[15,x]+F[16,x]+F[19,x]<br />
  
    F[15,x] = 0<br />
  
    F[16,x] = F[17,x]*F[4,x]<br />
  
    F[17,x] = F[18,x]+F[4,x]<br />
  
    F[18,x] = F[16,x]<br />
  
    F[19,x] = F[13,x]*F[4,x]<br />
  
    F[20,x] = F[2,x]+F[21,x]<br />
  
    F[21,x] = F[15,x]+F[22,x]+F[66,x]<br />
  
    F[22,x] = F[23,x]*F[4,x]<br />
  
    F[23,x] = F[24,x]+F[38,x]<br />
  
    F[24,x] = F[25,x]+F[28,x]<br />
  
    F[25,x] = F[26,x]<br />
  
    F[26,x] = F[27,x]*F[4,x]<br />
  
    F[27,x] = F[1,x]+F[4,x]<br />
  
    F[28,x] = F[15,x]+F[29,x]+F[36,x]<br />
  
    F[29,x] = F[30,x]*F[4,x]<br />
  
    F[30,x] = F[17,x]+F[31,x]<br />
  
    F[31,x] = F[32,x]+F[34,x]<br />
  
    F[32,x] = F[33,x]<br />
  
    F[33,x] = F[11,x]*F[4,x]<br />
  
    F[34,x] = F[35,x]<br />
  
    F[35,x] = F[31,x]*F[4,x]<br />
  
    F[36,x] = F[37,x]*F[4,x]<br />
  
    F[37,x] = F[11,x]+F[18,x]<br />
  
    F[38,x] = F[39,x]+F[44,x]<br />
  
    F[39,x] = F[40,x]<br />
  
    F[40,x] = F[4,x]*F[41,x]<br />
  
    F[41,x] = F[2,x]+F[42,x]<br />
  
    F[42,x] = F[43,x]<br />
  
    F[43,x] = F[2,x]*F[4,x]<br />
  
    F[44,x] = 2*F[15,x]+F[45,x]+F[64,x]<br />
  
    F[45,x] = F[4,x]*F[46,x]<br />
  
    F[46,x] = F[47,x]+F[50,x]<br />
  
    F[47,x] = F[42,x]+F[48,x]<br />
  
    F[48,x] = F[49,x]<br />
  
    F[49,x] = F[4,x]*F[47,x]<br />
  
    F[50,x] = F[51,x]+F[62,x]<br />
  
    F[51,x] = F[52,x]<br />
  
    F[52,x] = F[4,x]*F[53,x]<br />
  
    F[53,x] = F[15,x]+F[54,x]+F[60,x]<br />
  
    F[54,x] = F[4,x]*F[55,x]<br />
  
    F[55,x] = F[56,x]+F[58,x]<br />
  
    F[56,x] = F[4,x]+F[57,x]<br />
  
    F[57,x] = F[15,x]+F[29,x]+F[33,x]<br />
  
    F[58,x] = F[42,x]+F[59,x]<br />
  
    F[59,x] = 2*F[15,x]+F[45,x]+F[52,x]<br />
  
    F[60,x] = F[4,x]*F[61,x]<br />
  
    F[61,x] = F[2,x]+F[53,x]<br />
  
    F[62,x] = F[63,x]<br />
  
    F[63,x] = F[4,x]*F[50,x]<br />
  
    F[64,x] = F[4,x]*F[65,x]<br />
  
    F[65,x] = F[48,x]+F[53,x]<br />
  
    F[66,x] = F[4,x]*F[67,x]<br />
  
    F[67,x] = F[61,x]+F[68,x]<br />
  
    F[68,x] = F[53,x]+F[69,x]<br />
  
    F[69,x] = F[15,x]+F[49,x]+F[70,x]+F[82,x]<br />
  
    F[70,x] = F[4,x]*F[71,x]<br />
  
    F[71,x] = F[72,x]+F[77,x]<br />
  
    F[72,x] = F[73,x]+F[75,x]<br />
  
    F[73,x] = F[74,x]<br />
  
    F[74,x] = x^2<br />
  
    F[75,x] = F[76,x]<br />
  
    F[76,x] = F[18,x]*F[4,x]<br />
  
    F[77,x] = F[78,x]+F[80,x]<br />
  
    F[78,x] = F[79,x]<br />
  
    F[79,x] = F[4,x]*F[42,x]<br />
  
    F[80,x] = F[81,x]<br />
  
    F[81,x] = F[4,x]*F[48,x]<br />
  
    F[82,x] = F[4,x]*F[68,x]<br />
  
  System of equations in latex syntax:<br />
  
    F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{1}\! \left(x \right) = 1<br />
  
    F_{2}\! \left(x \right) = F_{3}\! \left(x \right)<br />
  
    F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = x<br />
  
    F_{5}\! \left(x \right) = F_{20}\! \left(x \right)+F_{6}\! \left(x \right)<br />
  
    F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{7}\! \left(x \right) = F_{8}\! \left(x \right)<br />
  
    F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)<br />
  
    F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)<br />
  
    F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)<br />
  
    F_{11}\! \left(x \right) = F_{12}\! \left(x \right)<br />
  
    F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{13}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{19}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = 0<br />
  
    F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = F_{16}\! \left(x \right)<br />
  
    F_{19}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)<br />
  
    F_{21}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)+F_{66}\! \left(x \right)<br />
  
    F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{38}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)<br />
  
    F_{25}\! \left(x \right) = F_{26}\! \left(x \right)<br />
  
    F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{36}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{17}\! \left(x \right)+F_{31}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{34}\! \left(x \right)<br />
  
    F_{32}\! \left(x \right) = F_{33}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{35}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{44}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{40}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = F_{2}\! \left(x \right)+F_{42}\! \left(x \right)<br />
  
    F_{42}\! \left(x \right) = F_{43}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{45}\! \left(x \right)+F_{64}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{42}\! \left(x \right)+F_{48}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{49}\! \left(x \right)<br />
  
    F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)<br />
  
    F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{62}\! \left(x \right)<br />
  
    F_{51}\! \left(x \right) = F_{52}\! \left(x \right)<br />
  
    F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{15}\! \left(x \right)+F_{54}\! \left(x \right)+F_{60}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)<br />
  
    F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{58}\! \left(x \right)<br />
  
    F_{56}\! \left(x \right) = F_{4}\! \left(x \right)+F_{57}\! \left(x \right)<br />
  
    F_{57}\! \left(x \right) = F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{33}\! \left(x \right)<br />
  
    F_{58}\! \left(x \right) = F_{42}\! \left(x \right)+F_{59}\! \left(x \right)<br />
  
    F_{59}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{45}\! \left(x \right)+F_{52}\! \left(x \right)<br />
  
    F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)<br />
  
    F_{61}\! \left(x \right) = F_{2}\! \left(x \right)+F_{53}\! \left(x \right)<br />
  
    F_{62}\! \left(x \right) = F_{63}\! \left(x \right)<br />
  
    F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)<br />
  
    F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)<br />
  
    F_{65}\! \left(x \right) = F_{48}\! \left(x \right)+F_{53}\! \left(x \right)<br />
  
    F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)<br />
  
    F_{67}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)<br />
  
    F_{68}\! \left(x \right) = F_{53}\! \left(x \right)+F_{69}\! \left(x \right)<br />
  
    F_{69}\! \left(x \right) = F_{15}\! \left(x \right)+F_{49}\! \left(x \right)+F_{70}\! \left(x \right)+F_{82}\! \left(x \right)<br />
  
    F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)<br />
  
    F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{77}\! \left(x \right)<br />
  
    F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{75}\! \left(x \right)<br />
  
    F_{73}\! \left(x \right) = F_{74}\! \left(x \right)<br />
  
    F_{74}\! \left(x \right) = x^{2}<br />
  
    F_{75}\! \left(x \right) = F_{76}\! \left(x \right)<br />
  
    F_{76}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{80}\! \left(x \right)<br />
  
    F_{78}\! \left(x \right) = F_{79}\! \left(x \right)<br />
  
    F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)<br />
  
    F_{80}\! \left(x \right) = F_{81}\! \left(x \right)<br />
  
    F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)<br />
  
    F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)<br />
  
  System of equations in sympy syntax:<br />
  
    Eq(F_0(x), F_1(x) + F_2(x))<br />
  
    Eq(F_1(x), 1)<br />
  
    Eq(F_2(x), F_3(x))<br />
  
    Eq(F_3(x), F_4(x)*F_5(x))<br />
  
    Eq(F_4(x), x)<br />
  
    Eq(F_5(x), F_20(x) + F_6(x))<br />
  
    Eq(F_6(x), F_1(x) + F_7(x))<br />
  
    Eq(F_7(x), F_8(x))<br />
  
    Eq(F_8(x), F_4(x)*F_9(x))<br />
  
    Eq(F_9(x), F_10(x) + F_13(x))<br />
  
    Eq(F_10(x), F_1(x) + F_11(x))<br />
  
    Eq(F_11(x), F_12(x))<br />
  
    Eq(F_12(x), F_10(x)*F_4(x))<br />
  
    Eq(F_13(x), F_11(x) + F_14(x))<br />
  
    Eq(F_14(x), F_15(x) + F_16(x) + F_19(x))<br />
  
    Eq(F_15(x), 0)<br />
  
    Eq(F_16(x), F_17(x)*F_4(x))<br />
  
    Eq(F_17(x), F_18(x) + F_4(x))<br />
  
    Eq(F_18(x), F_16(x))<br />
  
    Eq(F_19(x), F_13(x)*F_4(x))<br />
  
    Eq(F_20(x), F_2(x) + F_21(x))<br />
  
    Eq(F_21(x), F_15(x) + F_22(x) + F_66(x))<br />
  
    Eq(F_22(x), F_23(x)*F_4(x))<br />
  
    Eq(F_23(x), F_24(x) + F_38(x))<br />
  
    Eq(F_24(x), F_25(x) + F_28(x))<br />
  
    Eq(F_25(x), F_26(x))<br />
  
    Eq(F_26(x), F_27(x)*F_4(x))<br />
  
    Eq(F_27(x), F_1(x) + F_4(x))<br />
  
    Eq(F_28(x), F_15(x) + F_29(x) + F_36(x))<br />
  
    Eq(F_29(x), F_30(x)*F_4(x))<br />
  
    Eq(F_30(x), F_17(x) + F_31(x))<br />
  
    Eq(F_31(x), F_32(x) + F_34(x))<br />
  
    Eq(F_32(x), F_33(x))<br />
  
    Eq(F_33(x), F_11(x)*F_4(x))<br />
  
    Eq(F_34(x), F_35(x))<br />
  
    Eq(F_35(x), F_31(x)*F_4(x))<br />
  
    Eq(F_36(x), F_37(x)*F_4(x))<br />
  
    Eq(F_37(x), F_11(x) + F_18(x))<br />
  
    Eq(F_38(x), F_39(x) + F_44(x))<br />
  
    Eq(F_39(x), F_40(x))<br />
  
    Eq(F_40(x), F_4(x)*F_41(x))<br />
  
    Eq(F_41(x), F_2(x) + F_42(x))<br />
  
    Eq(F_42(x), F_43(x))<br />
  
    Eq(F_43(x), F_2(x)*F_4(x))<br />
  
    Eq(F_44(x), 2*F_15(x) + F_45(x) + F_64(x))<br />
  
    Eq(F_45(x), F_4(x)*F_46(x))<br />
  
    Eq(F_46(x), F_47(x) + F_50(x))<br />
  
    Eq(F_47(x), F_42(x) + F_48(x))<br />
  
    Eq(F_48(x), F_49(x))<br />
  
    Eq(F_49(x), F_4(x)*F_47(x))<br />
  
    Eq(F_50(x), F_51(x) + F_62(x))<br />
  
    Eq(F_51(x), F_52(x))<br />
  
    Eq(F_52(x), F_4(x)*F_53(x))<br />
  
    Eq(F_53(x), F_15(x) + F_54(x) + F_60(x))<br />
  
    Eq(F_54(x), F_4(x)*F_55(x))<br />
  
    Eq(F_55(x), F_56(x) + F_58(x))<br />
  
    Eq(F_56(x), F_4(x) + F_57(x))<br />
  
    Eq(F_57(x), F_15(x) + F_29(x) + F_33(x))<br />
  
    Eq(F_58(x), F_42(x) + F_59(x))<br />
  
    Eq(F_59(x), 2*F_15(x) + F_45(x) + F_52(x))<br />
  
    Eq(F_60(x), F_4(x)*F_61(x))<br />
  
    Eq(F_61(x), F_2(x) + F_53(x))<br />
  
    Eq(F_62(x), F_63(x))<br />
  
    Eq(F_63(x), F_4(x)*F_50(x))<br />
  
    Eq(F_64(x), F_4(x)*F_65(x))<br />
  
    Eq(F_65(x), F_48(x) + F_53(x))<br />
  
    Eq(F_66(x), F_4(x)*F_67(x))<br />
  
    Eq(F_67(x), F_61(x) + F_68(x))<br />
  
    Eq(F_68(x), F_53(x) + F_69(x))<br />
  
    Eq(F_69(x), F_15(x) + F_49(x) + F_70(x) + F_82(x))<br />
  
    Eq(F_70(x), F_4(x)*F_71(x))<br />
  
    Eq(F_71(x), F_72(x) + F_77(x))<br />
  
    Eq(F_72(x), F_73(x) + F_75(x))<br />
  
    Eq(F_73(x), F_74(x))<br />
  
    Eq(F_74(x), x**2)<br />
  
    Eq(F_75(x), F_76(x))<br />
  
    Eq(F_76(x), F_18(x)*F_4(x))<br />
  
    Eq(F_77(x), F_78(x) + F_80(x))<br />
  
    Eq(F_78(x), F_79(x))<br />
  
    Eq(F_79(x), F_4(x)*F_42(x))<br />
  
    Eq(F_80(x), F_81(x))<br />
  
    Eq(F_81(x), F_4(x)*F_48(x))<br />
  
    Eq(F_82(x), F_4(x)*F_68(x))<br />
  
  Pack JSON:<br />{&#34;expansion_strats&#34;: [[{&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;extra_basis&#34;: [], &#34;ignore_parent&#34;: false, &#34;maxreqlen&#34;: 1, &#34;one_cell_only&#34;: false, &#34;strategy_class&#34;: &#34;CellInsertionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;point_only&#34;: false, &#34;strategy_class&#34;: &#34;PatternPlacementFactory&#34;}]], &#34;inferral_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.row_and_col_separation&#34;, &#34;ignore_parent&#34;: true, &#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.obstruction_inferral&#34;, &#34;strategy_class&#34;: &#34;ObstructionTransitivityFactory&#34;}], &#34;initial_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;interleaving&#34;: null, &#34;strategy_class&#34;: &#34;FactorFactory&#34;, &#34;tracked&#34;: false, &#34;unions&#34;: false, &#34;workable&#34;: true}], &#34;iterative&#34;: false, &#34;name&#34;: &#34;point_placements&#34;, &#34;symmetries&#34;: [], &#34;ver_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;InsertionEncodingVerificationStrategy&#34;}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;OneByOneVerificationStrategy&#34;, &#34;symmetry&#34;: false}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;LocallyFactorableVerificationStrategy&#34;, &#34;symmetry&#34;: false}]}<br />
  Specification JSON:<br />{&#34;root&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], 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{&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: 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2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], 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[0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], 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[0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], 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[[0, 0], [0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], 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{&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 0], [1, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, 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&#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 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[1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 1], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], 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{&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0], 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{&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], 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[0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 1], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], 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&#34;pos&#34;: [[1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 1], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 1], [1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 1], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 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&#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 1], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 5]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 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[1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 3], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, &#34;rule_class&#34;: &#34;EquivalenceRule&#34;}]}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.strategy&#34;, &#34;strategy_class&#34;: &#34;EmptyStrategy&#34;}}]}<br /><br />