01243_01342_01432_02143_02341_02431_03142_03241_03421_04132_04231_04321_10243_10342_10432_12043_12340_12430_13042_13240_13420_14032_14230_14320_20143_20341_20431_21043_21340_21430_23041_23140_24031_24130_30142_30241_31042_31240_32041_32140
Counting sequence:
1, 1, 2, 6, 24, 80, 252, 794, 2522, 8034, 25590, 81472, 259346, 825572, 2628098, 8366266, 26633084, 84783360, 269897962, 859188804, 2735127952, 8706962944, 27717607650, 88235791902, 280888418006, 894175727182, 2846504804128, 9061518171526, 28846292988044, 91828830819490, 292326441152922, 930587348598464, 2962416981360732, 9430511154780854, 30020939388347360, 95568181508580432, 304230230730287916, 968481683225232442, 3083049204187460258, 9814529856452003786, 31243418422371332654, 99459801844064617720, 316618753080406076882, 1007919108459128092524, 3208593677137794791362, 10214186137127003978514, 32515677876964468071220, 103509892379531282581312, 329511746947543315790826, 1048962460305801050937852, 3339250431354015584799488, 10630116772765422195077296, 33839744854598764757120914, 107724906160785167750568550, 342929754855197051502095342, 1091677133508197766977663734, 3475227643421897470604741592, 11062984469403126125967455174, 35217729003140441846314366980, 112111559007327786687737135042, 356894155836474715264096155986, 1136131185740665439211196269912, 3616741967060730441906166081068, 11513478919048143057890818088806, 36651825877170771122102043486824, 116676840212732558364999412562480, 371427199497499575985588761385052, 1182395446045859152811092400053594, 3764018878319647309724441079226922, 11982317898573162258923178049098834, 38144320436183007311352334527952390, 121428023680749339504738499680625872, 386552041467908995175085923334620146, 1230543627687294831551570761304416372, 3917293034830647890461017413706270498, 12470248413355904742778992865731105066, 39697590685228972257094133339436831884, 126372679514880921972272150797072233760, 402292780294928126075456577954596542762, 1280652445597357318427521771514706183604, 4076808649690722042540851040295025950352, 12978047887489533907970917200603035923744, 41314111463815967368721582118908831856450, 131518686079897269964884815997535960944302, 418674495839802716010796207520348359408806, 1332801738607894557560762414970915656569982, 4242819880568781317330356196315352599564528, 13506525402459480044357396873979616737700326, 42996458389090897995597845496581543066318844, 136874242554505216489090614816680855256797890, 435723289237768394883538416513642807856347722, 1387074596658148986336677737385480691544805264, 4415591234657366810541012736861963207728671132, 14056522986260273671612677272885070403365301654, 44747311959594320579778091119072563463786538160, 142447881995173901051307106095021517679205230832, 453466324485225029559589181495021754289470248716, 1443557493182707683010875755848861926513905797242, 4595397990114346425248787902687090049296049228658, 14628916955006349195479725600319664315647146062586, 46569461826122960950816563282407431333110172115454
Generating function in Maple syntax:
(x-1)*(2*x^5-3*x^4+2*x^3-2*x^2+3*x-1)/(3*x^4-8*x^3+8*x^2-5*x+1)
Generating function in latex syntax:
\frac{\left(x -1\right) \left(2 x^{5}-3 x^{4}+2 x^{3}-2 x^{2}+3 x -1\right)}{3 x^{4}-8 x^{3}+8 x^{2}-5 x +1}
Generating function in sympy syntax:
(x - 1)*(2*x**5 - 3*x**4 + 2*x**3 - 2*x**2 + 3*x - 1)/(3*x**4 - 8*x**3 + 8*x**2 - 5*x + 1)
Implicit equation for the generating function in Maple syntax:
(-3*x^4+8*x^3-8*x^2+5*x-1)*F(x)+(x-1)*(2*x^5-3*x^4+2*x^3-2*x^2+3*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(-3 x^{4}+8 x^{3}-8 x^{2}+5 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(2 x^{5}-3 x^{4}+2 x^{3}-2 x^{2}+3 x -1\right) = 0
Explicit closed form in Maple syntax:
-2350/6729*Sum(_alpha^(2-n),_alpha = RootOf(3*_Z^4-8*_Z^3+8*_Z^2-5*_Z+1))+844/6729*Sum(_alpha^(1-n),_alpha = RootOf(3*_Z^4-8*_Z^3+8*_Z^2-5*_Z+1))+2030/6729*Sum(_alpha^(-n),_alpha = RootOf(3*_Z^4-8*_Z^3+8*_Z^2-5*_Z+1))-142/6729*Sum(_alpha^(-n-1),_alpha = RootOf(3*_Z^4-8*_Z^3+8*_Z^2-5*_Z+1))+1/3*piecewise(n = 0,5/9,n = 1,1/3,n = 2,2,0)
Explicit closed form in latex syntax:
-\frac{2350 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{4}-8 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{2-n}\right)}{6729}+\frac{844 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{4}-8 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{1-n}\right)}{6729}+\frac{2030 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{4}-8 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{6729}-\frac{142 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{4}-8 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{6729}+\frac{\left(\left\{\begin{array}{cc}\frac{5}{9} & n =0 \\ \frac{1}{3} & n =1 \\ 2 & n =2 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)}{3}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a(6) = 252
a(n+4) = -3*a(n)+8*a(n+1)-8*a(n+2)+5*a(n+3), n >= 7
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a(6) = 252
a{\left(n + 4 \right)} = - 3 a{\left(n \right)} + 8 a{\left(n + 1 \right)} - 8 a{\left(n + 2 \right)} + 5 a{\left(n + 3 \right)}, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/24469/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[16,x]*F[4,x]
F[4,x] = F[38,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[22,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[16,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = x
F[17,x] = F[16,x]+F[18,x]
F[18,x] = F[19,x]+F[20,x]+F[21,x]
F[19,x] = 0
F[20,x] = F[14,x]*F[16,x]
F[21,x] = F[16,x]*F[17,x]
F[22,x] = F[23,x]+F[28,x]
F[23,x] = F[24,x]
F[24,x] = F[16,x]*F[25,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[1,x]+F[16,x]
F[27,x] = F[16,x]
F[28,x] = F[19,x]+F[29,x]+F[33,x]
F[29,x] = F[16,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[14,x]+F[18,x]
F[32,x] = F[18,x]
F[33,x] = F[16,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[23,x]+F[36,x]
F[36,x] = F[19,x]+F[29,x]+F[37,x]
F[37,x] = F[16,x]*F[35,x]
F[38,x] = F[39,x]+F[56,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[1,x]+F[23,x]
F[43,x] = F[39,x]+F[44,x]
F[44,x] = F[19,x]+F[45,x]+F[51,x]
F[45,x] = F[16,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[16,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[16,x]*F[39,x]
F[51,x] = F[16,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[39,x]+F[49,x]
F[54,x] = F[55,x]
F[55,x] = F[19,x]+F[45,x]+F[50,x]
F[56,x] = F[19,x]+F[57,x]+F[92,x]
F[57,x] = F[16,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[10,x]+F[28,x]
F[60,x] = F[61,x]+F[89,x]
F[61,x] = F[19,x]+F[62,x]+F[87,x]
F[62,x] = F[16,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[14,x]+F[36,x]
F[65,x] = F[66,x]+F[69,x]
F[66,x] = F[19,x]+F[62,x]+F[67,x]
F[67,x] = F[16,x]*F[68,x]
F[68,x] = F[39,x]+F[66,x]
F[69,x] = F[19,x]+F[70,x]+F[78,x]+F[85,x]
F[70,x] = F[16,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[18,x]
F[73,x] = F[74,x]
F[74,x] = 2*F[19,x]+F[75,x]+F[76,x]
F[75,x] = F[16,x]*F[66,x]
F[76,x] = F[16,x]*F[77,x]
F[77,x] = F[49,x]+F[74,x]
F[78,x] = F[16,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[66,x]+F[74,x]
F[81,x] = F[82,x]
F[82,x] = F[19,x]+F[70,x]+F[75,x]+F[83,x]
F[83,x] = F[16,x]*F[84,x]
F[84,x] = F[55,x]+F[82,x]
F[85,x] = F[16,x]*F[86,x]
F[86,x] = F[44,x]+F[69,x]
F[87,x] = F[16,x]*F[88,x]
F[88,x] = F[68,x]+F[77,x]
F[89,x] = F[19,x]+F[70,x]+F[78,x]+F[90,x]
F[90,x] = F[16,x]*F[91,x]
F[91,x] = F[86,x]
F[92,x] = F[16,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[39,x]+F[61,x]
F[95,x] = F[44,x]+F[89,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{38}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{22}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{16}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right)+F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{23}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{19}\! \left(x \right)+F_{29}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{56}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)+F_{51}\! \left(x \right)
F_{45}\! \left(x \right) = F_{16}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{16}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{51}\! \left(x \right) = F_{16}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{39}\! \left(x \right)+F_{49}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)+F_{50}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right)+F_{57}\! \left(x \right)+F_{92}\! \left(x \right)
F_{57}\! \left(x \right) = F_{16}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{10}\! \left(x \right)+F_{28}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{89}\! \left(x \right)
F_{61}\! \left(x \right) = F_{19}\! \left(x \right)+F_{62}\! \left(x \right)+F_{87}\! \left(x \right)
F_{62}\! \left(x \right) = F_{16}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right)+F_{36}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{69}\! \left(x \right)
F_{66}\! \left(x \right) = F_{19}\! \left(x \right)+F_{62}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{16}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{39}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right)+F_{70}\! \left(x \right)+F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{70}\! \left(x \right) = F_{16}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{18}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{16}\! \left(x \right) F_{66}\! \left(x \right)
F_{76}\! \left(x \right) = F_{16}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{49}\! \left(x \right)+F_{74}\! \left(x \right)
F_{78}\! \left(x \right) = F_{16}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{66}\! \left(x \right)+F_{74}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{19}\! \left(x \right)+F_{70}\! \left(x \right)+F_{75}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{16}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{55}\! \left(x \right)+F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{16}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{44}\! \left(x \right)+F_{69}\! \left(x \right)
F_{87}\! \left(x \right) = F_{16}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{68}\! \left(x \right)+F_{77}\! \left(x \right)
F_{89}\! \left(x \right) = F_{19}\! \left(x \right)+F_{70}\! \left(x \right)+F_{78}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{16}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{86}\! \left(x \right)
F_{92}\! \left(x \right) = F_{16}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{39}\! \left(x \right)+F_{61}\! \left(x \right)
F_{95}\! \left(x \right) = F_{44}\! \left(x \right)+F_{89}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_16(x)*F_4(x))
Eq(F_4(x), F_38(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_22(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_16(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), x)
Eq(F_17(x), F_16(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_21(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_14(x)*F_16(x))
Eq(F_21(x), F_16(x)*F_17(x))
Eq(F_22(x), F_23(x) + F_28(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_16(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_1(x) + F_16(x))
Eq(F_27(x), F_16(x))
Eq(F_28(x), F_19(x) + F_29(x) + F_33(x))
Eq(F_29(x), F_16(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_14(x) + F_18(x))
Eq(F_32(x), F_18(x))
Eq(F_33(x), F_16(x)*F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_23(x) + F_36(x))
Eq(F_36(x), F_19(x) + F_29(x) + F_37(x))
Eq(F_37(x), F_16(x)*F_35(x))
Eq(F_38(x), F_39(x) + F_56(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_1(x) + F_23(x))
Eq(F_43(x), F_39(x) + F_44(x))
Eq(F_44(x), F_19(x) + F_45(x) + F_51(x))
Eq(F_45(x), F_16(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_16(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_16(x)*F_39(x))
Eq(F_51(x), F_16(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_39(x) + F_49(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_19(x) + F_45(x) + F_50(x))
Eq(F_56(x), F_19(x) + F_57(x) + F_92(x))
Eq(F_57(x), F_16(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_10(x) + F_28(x))
Eq(F_60(x), F_61(x) + F_89(x))
Eq(F_61(x), F_19(x) + F_62(x) + F_87(x))
Eq(F_62(x), F_16(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_14(x) + F_36(x))
Eq(F_65(x), F_66(x) + F_69(x))
Eq(F_66(x), F_19(x) + F_62(x) + F_67(x))
Eq(F_67(x), F_16(x)*F_68(x))
Eq(F_68(x), F_39(x) + F_66(x))
Eq(F_69(x), F_19(x) + F_70(x) + F_78(x) + F_85(x))
Eq(F_70(x), F_16(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_18(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), 2*F_19(x) + F_75(x) + F_76(x))
Eq(F_75(x), F_16(x)*F_66(x))
Eq(F_76(x), F_16(x)*F_77(x))
Eq(F_77(x), F_49(x) + F_74(x))
Eq(F_78(x), F_16(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_66(x) + F_74(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_19(x) + F_70(x) + F_75(x) + F_83(x))
Eq(F_83(x), F_16(x)*F_84(x))
Eq(F_84(x), F_55(x) + F_82(x))
Eq(F_85(x), F_16(x)*F_86(x))
Eq(F_86(x), F_44(x) + F_69(x))
Eq(F_87(x), F_16(x)*F_88(x))
Eq(F_88(x), F_68(x) + F_77(x))
Eq(F_89(x), F_19(x) + F_70(x) + F_78(x) + F_90(x))
Eq(F_90(x), F_16(x)*F_91(x))
Eq(F_91(x), F_86(x))
Eq(F_92(x), F_16(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_39(x) + F_61(x))
Eq(F_95(x), F_44(x) + F_89(x))
Pack JSON:
{"name": "point_placements", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], 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