0132_0231_0321_1023
Counting sequence:
1, 1, 2, 6, 20, 65, 210, 679, 2196, 7102, 22968, 74279, 240220, 776877, 2512438, 8125282, 26277348, 84981545, 274832262, 888813827, 2874444264, 9296018554, 30063536816, 97226166303, 314431647608, 1016879146601, 3288610439370, 10635441446590, 34395261113844, 111235061847745, 359736736503258, 1163396841250895, 3762452018075452, 12167855959707894, 39351124730603752, 127262438238191335, 411569638662294420, 1331025633436103285, 4304567369503308798, 13921069416791322842, 45021057186865277124, 145599129602657654281, 470870918314114122638, 1522807329405422759115, 4924793764697798699984, 15926895777600497113586, 51507945556805323749984, 166577875094409978300031, 538716661497727137477360, 1742222016043688765395729, 5634385884313588282000914, 18221732937024331128471158, 58929501465746210061195988, 190579356804495334657976577, 616338002810477782423259746, 1993251210822893214713030071, 6446220047003383970837098212, 20847223204361316469397845550, 67420397095270422612082887960, 218039107651181615767099181543, 705143465680634444200106655180, 2280450110755172458253897006461, 7375027864185879309337383535430, 23851008948188087135220957251154, 77134708956024421085179365756068, 249455414597150009095475461335209, 806744521552717068087468279039510, 2609030251383279000098584506413395, 8437663561113240393237704745449400, 27287597118811408699734526559301226, 88248713773119754551334692734643984, 285398360606887993892512016245157663, 922984831784702288922275335149851752, 2984954075745573274414500150773920761, 9653409815068842464124863937401799130, 31219348336001166617207993951339980078, 100964087218504583336364108959552512692, 326520169420406945147667681708219788033, 1055973702883047521351869523919499775082, 3415043129371977250019995274521104781535, 11044327660461075742983343780782806864268, 35717608490074059319429460665698692874598, 115511563534773917027455932345569060693576, 373567040860423664387482039672224673097511, 1208124362157059949363435939202806089194244, 3907101844626442579026780041819989765996997, 12635656810220663879764320496670421081906702, 40864003390457024016316331699955102534926794, 132155122458261929634662489454246320336786820, 427392691437491531670202823668640826140183305, 1382197748345873721929692169215064127538319646, 4470059160597087127961168853062871569871375515, 14456273657767448479761342062489329228814122912, 46751919954532788447351043205530189634578821090, 151196779417677108884112792171563449864077347008, 488973845962047880025959554341579017440329795071, 1581352611846458321866440585200196770209430658528, 5114130548380511076708758218913646738610309121825, 16539215270489087992403517436565591228829526754850, 53488200814545687503194716705580239222465711175910, 172982065931630049867119390365251279910385452024212
Generating function in Maple syntax:
(x^4-x^3+x^2-3*x+1)/(x^4-2*x^3+3*x^2-4*x+1)
Generating function in latex syntax:
\frac{x^{4}-x^{3}+x^{2}-3 x +1}{x^{4}-2 x^{3}+3 x^{2}-4 x +1}
Generating function in sympy syntax:
(x**4 - x**3 + x**2 - 3*x + 1)/(x**4 - 2*x**3 + 3*x**2 - 4*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^4-2*x^3+3*x^2-4*x+1)*F(x)-x^4+x^3-x^2+3*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{4}-2 x^{3}+3 x^{2}-4 x +1\right) F \! \left(x \right)-x^{4}+x^{3}-x^{2}+3 x -1 = 0
Explicit closed form in Maple syntax:
-7/61*Sum(_alpha^(-n+2),_alpha = RootOf(_Z^4-2*_Z^3+3*_Z^2-4*_Z+1))+19/61*Sum(_alpha^(-n+1),_alpha = RootOf(_Z^4-2*_Z^3+3*_Z^2-4*_Z+1))-43/122*Sum(_alpha^(-n),_alpha = RootOf(_Z^4-2*_Z^3+3*_Z^2-4*_Z+1))+17/122*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^4-2*_Z^3+3*_Z^2-4*_Z+1))+piecewise(n = 0,1,0)
Explicit closed form in latex syntax:
-\frac{7 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+3 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{61}+\frac{19 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+3 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{61}-\frac{43 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+3 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{122}+\frac{17 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+3 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{122}+\left(\left\{\begin{array}{cc}1 & n =0 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n+4) = -a(n)+2*a(n+1)-3*a(n+2)+4*a(n+3), n >= 5
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) = 20
a \! \left(n +4\right) = -a \! \left(n \right)+2 a \! \left(n +1\right)-3 a \! \left(n +2\right)+4 a \! \left(n +3\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15310/
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[18,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[11,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[4,x]
F[17,x] = F[15,x]
F[18,x] = F[19,x]+F[2,x]
F[19,x] = F[20,x]+F[21,x]+F[87,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[33,x]
F[23,x] = F[24,x]+F[27,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[1,x]+F[4,x]
F[27,x] = F[20,x]+F[28,x]+F[31,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[16,x]+F[30,x]
F[30,x] = F[17,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[11,x]+F[17,x]
F[33,x] = F[34,x]+F[68,x]
F[34,x] = F[20,x]+F[21,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[20,x]+F[38,x]+F[67,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[4,x]+F[41,x]
F[41,x] = F[20,x]+F[28,x]+F[42,x]
F[42,x] = F[11,x]*F[4,x]
F[43,x] = F[37,x]+F[44,x]
F[44,x] = F[20,x]+F[45,x]+F[60,x]+F[63,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[52,x]
F[47,x] = F[48,x]+F[50,x]
F[48,x] = F[49,x]
F[49,x] = x^2
F[50,x] = F[51,x]
F[51,x] = F[17,x]*F[4,x]
F[52,x] = F[53,x]+F[55,x]
F[53,x] = 2*F[20,x]+F[45,x]+F[54,x]
F[54,x] = F[37,x]*F[4,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[37,x]+F[57,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[59,x]+F[62,x]
F[62,x] = F[57,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[20,x]+F[38,x]+F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[2,x]+F[64,x]
F[67,x] = F[2,x]*F[4,x]
F[68,x] = F[20,x]+F[60,x]+F[69,x]+F[85,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[78,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[4,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[17,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = 2*F[20,x]+F[69,x]+F[80,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[37,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[57,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[57,x]+F[64,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[66,x]+F[89,x]
F[89,x] = F[64,x]+F[90,x]
F[90,x] = F[58,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_{18}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{87}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{33}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{68}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \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_{20}\! \left(x \right)+F_{38}\! \left(x \right)+F_{67}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{20}\! \left(x \right)+F_{45}\! \left(x \right)+F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{52}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = x^{2}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{45}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{37}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \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_{2}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right)+F_{60}\! \left(x \right)+F_{69}\! \left(x \right)+F_{85}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{78}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{17}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{69}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{37}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{57}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{57}\! \left(x \right)+F_{64}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{66}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{64}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{58}\! \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_18(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_11(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_4(x))
Eq(F_17(x), F_15(x))
Eq(F_18(x), F_19(x) + F_2(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_87(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_33(x))
Eq(F_23(x), F_24(x) + F_27(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_1(x) + F_4(x))
Eq(F_27(x), F_20(x) + F_28(x) + F_31(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_16(x) + F_30(x))
Eq(F_30(x), F_17(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_11(x) + F_17(x))
Eq(F_33(x), F_34(x) + F_68(x))
Eq(F_34(x), F_20(x) + F_21(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_20(x) + F_38(x) + F_67(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_4(x) + F_41(x))
Eq(F_41(x), F_20(x) + F_28(x) + F_42(x))
Eq(F_42(x), F_11(x)*F_4(x))
Eq(F_43(x), F_37(x) + F_44(x))
Eq(F_44(x), F_20(x) + F_45(x) + F_60(x) + F_63(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_52(x))
Eq(F_47(x), F_48(x) + F_50(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), x**2)
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_17(x)*F_4(x))
Eq(F_52(x), F_53(x) + F_55(x))
Eq(F_53(x), 2*F_20(x) + F_45(x) + F_54(x))
Eq(F_54(x), F_37(x)*F_4(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_37(x) + F_57(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_59(x) + F_62(x))
Eq(F_62(x), F_57(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_20(x) + F_38(x) + F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_2(x) + F_64(x))
Eq(F_67(x), F_2(x)*F_4(x))
Eq(F_68(x), F_20(x) + F_60(x) + F_69(x) + F_85(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_78(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_4(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_17(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), 2*F_20(x) + F_69(x) + F_80(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_37(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_57(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_57(x) + F_64(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_66(x) + F_89(x))
Eq(F_89(x), F_64(x) + F_90(x))
Eq(F_90(x), F_58(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, 3, 2], "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": [1, 0, 2, 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, 3, 2], "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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": 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[0, 1]]}], "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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, 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