0123_0231_0321_2031_2103

Counting sequence:
1, 1, 2, 6, 19, 51, 121, 306, 814, 2149, 5556, 14302, 37094, 96554, 250860, 650529, 1687207, 4379386, 11369178, 29507507, 76573147, 198722405, 515760164, 1338589132, 3474037661, 9016101824, 23399522788, 60729184644, 157611184596, 409049149788, 1061607480813, 2755198444117, 7150590680730, 18557984903962, 48163676483983, 124999556501767, 324412331876945, 841949877451702, 2185119062957006, 5671056430381285, 14718136841150076, 38198095245048170, 99135814069803298, 257287949424094558, 667741416437603424, 1732994494277200573, 4497654098691842475, 11672796682737490210, 30294500059199912982, 78623551736602249079, 204052315647063796487, 529578562678853818757, 1374419364695632761232, 3567041272332582368916, 9257569971376513512173, 24026243385674601518080, 62355496421995489034376, 161831705090202152268872, 420003083531702706188024, 1090037270991469211695320, 2828982211654720072742793, 7342079547955233497156073, 19054956184030386126887362, 49453476062712976771435022, 128346991253402968043016907, 333099945146662958103752715, 864496879694184347805760425, 2243635479050900825218472746, 5822924617885005443571283646, 15112281572546163477410437381, 39221021963164316516543339780, 101790623503836229890603298742, 264177997274800812029598694910, 685623212058373868738063279522, 1779403257509976891518600255700, 4618099120844145651055858274153, 11985388584589506986295394211503, 31105772259247365155619760321562, 80729052797523614712236284229938, 209516738927704258077102612845243, 543760422917365656416824632300227, 1411225656930914491966418202316581, 3662564929045497757111355041908300, 9505483261016663485270002256254572, 24669654675313899140101621738807037, 64025346748561280999824443391148096, 166165480637046954838308053823285356, 431250564932883786685765731995373644, 1119227946995553228253156892187155948, 2904741000236918234560011804928527732, 7538696921486803329275331753075899797, 19565238783560821405139758953364049277, 50777816464102645478541110311783690362, 131784062202630280420453670330026400482, 342020202127130601704602637646587549575, 887647692049581620925901750600430851583, 2303718962507588101228248047937115215809, 5978859750046639623399779192625744450702, 15516981234472093993480703189056087875454, 40271342144976869510529940533705807383557, 104516527644880219643669799879574158304460

Generating function in Maple syntax:
-1/(5*x^6+12*x^5+8*x^4+3*x^3+x^2+x-1)

Generating function in latex syntax:
-\frac{1}{5 x^{6}+12 x^{5}+8 x^{4}+3 x^{3}+x^{2}+x -1}

Generating function in sympy syntax:
-1/(5*x**6 + 12*x**5 + 8*x**4 + 3*x**3 + x**2 + x - 1)

Implicit equation for the generating function in Maple syntax:
(5*x^6+12*x^5+8*x^4+3*x^3+x^2+x-1)*F(x)+1 = 0

Implicit equation for the generating function in latex syntax:
\left(5 x^{6}+12 x^{5}+8 x^{4}+3 x^{3}+x^{2}+x -1\right) F \! \left(x \right)+1 = 0

Explicit closed form in Maple syntax:
17028770/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n+4)+17028770/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n+4)+17028770/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n+4)+17028770/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n+4)+17028770/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n+4)+17028770/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n+4)+123793723/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n+3)+123793723/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n+3)+123793723/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n+3)+123793723/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n+3)+123793723/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n+3)+123793723/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n+3)+187685002/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n+2)+187685002/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n+2)+187685002/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n+2)+187685002/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n+2)+187685002/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n+2)+187685002/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n+2)+176225207/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n+1)+176225207/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n+1)+176225207/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n+1)+176225207/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n+1)+176225207/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n+1)+176225207/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n+1)+56746946/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n-1)+56746946/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n-1)+56746946/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n-1)+56746946/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n-1)+56746946/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n-1)+56746946/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n-1)+261813635/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n)+261813635/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n)+261813635/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n)+261813635/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n)+261813635/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n)+261813635/1285987569*RootOf(5*_Z^6+12*_Z^5+8*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n)

Explicit closed form in latex syntax:
\frac{17028770 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{1285987569}+\frac{17028770 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{1285987569}+\frac{17028770 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{1285987569}+\frac{17028770 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{1285987569}+\frac{17028770 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{1285987569}+\frac{17028770 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n +4}}{1285987569}+\frac{123793723 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{1285987569}+\frac{123793723 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{1285987569}+\frac{123793723 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{1285987569}+\frac{123793723 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{1285987569}+\frac{123793723 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{1285987569}+\frac{123793723 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n +3}}{1285987569}+\frac{187685002 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{1285987569}+\frac{187685002 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{1285987569}+\frac{187685002 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{1285987569}+\frac{187685002 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{1285987569}+\frac{187685002 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{1285987569}+\frac{187685002 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n +2}}{1285987569}+\frac{176225207 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{1285987569}+\frac{176225207 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{1285987569}+\frac{176225207 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{1285987569}+\frac{176225207 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{1285987569}+\frac{176225207 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{1285987569}+\frac{176225207 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n +1}}{1285987569}+\frac{56746946 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{1285987569}+\frac{56746946 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{1285987569}+\frac{56746946 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{1285987569}+\frac{56746946 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{1285987569}+\frac{56746946 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{1285987569}+\frac{56746946 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{1285987569}+\frac{261813635 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{1285987569}+\frac{261813635 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{1285987569}+\frac{261813635 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{1285987569}+\frac{261813635 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{1285987569}+\frac{261813635 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{1285987569}+\frac{261813635 \mathit{RootOf}\! \left(5 \textit{\_Z}^{6}+12 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{1285987569}

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(n+6) = 5*a(n)+12*a(n+1)+8*a(n+2)+3*a(n+3)+a(n+4)+a(n+5), n >= 6

Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 51
a \! \left(n +6\right) = 5 a \! \left(n \right)+12 a \! \left(n +1\right)+8 a \! \left(n +2\right)+3 a \! \left(n +3\right)+a \! \left(n +4\right)+a \! \left(n +5\right), \quad n \geq 6

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17151/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[20,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[11,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[48,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[29,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[11,x]
F[29,x] = F[30,x]+F[45,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[39,x]
F[33,x] = F[2,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[2,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[2,x]*F[4,x]
F[39,x] = F[40,x]+F[42,x]
F[40,x] = F[41,x]
F[41,x] = F[36,x]*F[4,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[34,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[34,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[71,x]
F[50,x] = F[2,x]+F[51,x]
F[51,x] = F[22,x]+F[52,x]+F[58,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[56,x]
F[54,x] = F[11,x]+F[55,x]
F[55,x] = F[27,x]
F[56,x] = F[34,x]+F[57,x]
F[57,x] = F[46,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[2,x]+F[60,x]
F[60,x] = F[22,x]+F[38,x]+F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[67,x]
F[63,x] = F[4,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[4,x]
F[67,x] = F[37,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[37,x]
F[71,x] = F[72,x]+F[80,x]
F[72,x] = F[22,x]+F[73,x]+F[79,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[77,x]
F[75,x] = F[15,x]+F[76,x]
F[76,x] = F[65,x]
F[77,x] = F[40,x]+F[78,x]
F[78,x] = F[69,x]
F[79,x] = F[4,x]*F[59,x]
F[80,x] = 2*F[22,x]+F[81,x]+F[85,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[17,x]
F[84,x] = F[42,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[34,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{20}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{48}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{45}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{39}\! \left(x \right)
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{34}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{34}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{71}\! \left(x \right)
F_{50}\! \left(x \right) = F_{2}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right)+F_{52}\! \left(x \right)+F_{58}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{27}\! \left(x \right)
F_{56}\! \left(x \right) = F_{34}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{46}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{2}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x \right)+F_{38}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{37}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{37}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{80}\! \left(x \right)
F_{72}\! \left(x \right) = F_{22}\! \left(x \right)+F_{73}\! \left(x \right)+F_{79}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = F_{15}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{65}\! \left(x \right)
F_{77}\! \left(x \right) = F_{40}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{69}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{81}\! \left(x \right)+F_{85}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{17}\! \left(x \right)
F_{84}\! \left(x \right) = F_{42}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{34}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_20(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_11(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_48(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_29(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_11(x))
Eq(F_29(x), F_30(x) + F_45(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_39(x))
Eq(F_33(x), F_2(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_2(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_2(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_42(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_36(x)*F_4(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_34(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_34(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_71(x))
Eq(F_50(x), F_2(x) + F_51(x))
Eq(F_51(x), F_22(x) + F_52(x) + F_58(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_56(x))
Eq(F_54(x), F_11(x) + F_55(x))
Eq(F_55(x), F_27(x))
Eq(F_56(x), F_34(x) + F_57(x))
Eq(F_57(x), F_46(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_2(x) + F_60(x))
Eq(F_60(x), F_22(x) + F_38(x) + F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_67(x))
Eq(F_63(x), F_4(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_4(x))
Eq(F_67(x), F_37(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_37(x))
Eq(F_71(x), F_72(x) + F_80(x))
Eq(F_72(x), F_22(x) + F_73(x) + F_79(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_77(x))
Eq(F_75(x), F_15(x) + F_76(x))
Eq(F_76(x), F_65(x))
Eq(F_77(x), F_40(x) + F_78(x))
Eq(F_78(x), F_69(x))
Eq(F_79(x), F_4(x)*F_59(x))
Eq(F_80(x), 2*F_22(x) + F_81(x) + F_85(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_17(x))
Eq(F_84(x), F_42(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_34(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}], "requirements": []}], "class_module": 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