0123_0231_1032_1203_3021
Counting sequence:
1, 1, 2, 6, 19, 49, 116, 271, 632, 1472, 3425, 7965, 18519, 43054, 100091, 232686, 540932, 1257517, 2923375, 6796025, 15798844, 36727859, 85381916, 198488876, 461430657, 1072696137, 2493715975, 5797186310, 13476823119, 31329812714, 72832978216, 169316132341, 393612253307, 915037473457, 2127204046100, 4945149444695, 11496077715344, 26725138302744, 62128408922241, 144431027876581, 335761404088007, 780550565433102, 1814559915999875, 4218340021221430, 9806450797097644, 22797232264849949, 52997135221575991, 123203391932125721, 286413137618075132, 665829764211549947, 1547866409330625300, 3598352837186851140, 8365155457110852769, 19446627106289481329, 45207923241833589591, 105095670970032658886, 244317793532720278807, 567969961899929108242, 1320369969604379426000, 3069487778546000340325, 7135693358329171277219, 16588474487499892577009, 38563524524387335516916, 89649317956491392673951, 208409379308199399565032, 484493026536002748864112, 1126309638948100840136225, 2618352243080496422245485, 6086930477881290335328119, 14150396586430979001629614, 32895681046610852756478091, 76473180444851890601503166, 177778575827764945293182932, 413285047640201907433020557, 960771171709927722314198975, 2233521995677144297369738745, 5192308691251779354913838844, 12070653254110977192316238019, 28060864375506517164490775116, 65233595309549376463753688156, 151649710431746072254595752257, 352542805051645981000770655577, 819562589600995174956874150375, 1905251869131439635123676892230, 4429173233243974536458053031519, 10296578551070039514083679460474, 23936641055853609104458609210616, 55645939298664722821666521742421, 129361114335356989770166026266507, 300728105464595132771623644525297, 699108027021736141596205402785300, 1625228984471375149015534945571815, 3778199004835248296625817675670144, 8783247072584730733442588538652104, 20418572192555070756091665210187841, 47467421437330999098015636228929461, 110348366999467586515306166805064807, 256528830316295832105978893167523342, 596357178387283322385339982121369875, 1386362241528725889459368326834127750, 3222901198127906855713403909427166844
Generating function in Maple syntax:
(x^7-x^6-2*x^5+3*x^4+3*x^2-3*x+1)/(x-1)/(x^3-2*x^2+3*x-1)
Generating function in latex syntax:
\frac{x^{7}-x^{6}-2 x^{5}+3 x^{4}+3 x^{2}-3 x +1}{\left(x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right)}
Generating function in sympy syntax:
(x**7 - x**6 - 2*x**5 + 3*x**4 + 3*x**2 - 3*x + 1)/((x - 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
-(x-1)*(x^3-2*x^2+3*x-1)*F(x)+x^7-x^6-2*x^5+3*x^4+3*x^2-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) F \! \left(x \right)+x^{7}-x^{6}-2 x^{5}+3 x^{4}+3 x^{2}-3 x +1 = 0
Explicit closed form in Maple syntax:
-106/23*Sum(_alpha^(2-n),_alpha = RootOf(_Z^4-3*_Z^3+5*_Z^2-4*_Z+1))+185/23*Sum(_alpha^(1-n),_alpha = RootOf(_Z^4-3*_Z^3+5*_Z^2-4*_Z+1))-187/23*Sum(_alpha^(-n),_alpha = RootOf(_Z^4-3*_Z^3+5*_Z^2-4*_Z+1))+62/23*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^4-3*_Z^3+5*_Z^2-4*_Z+1))+piecewise(n = 0,-6,n = 1,-1,n = 2,2,n = 3,1,0)
Explicit closed form in latex syntax:
-\frac{106 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{2-n}\right)}{23}+\frac{185 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{1-n}\right)}{23}-\frac{187 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{23}+\frac{62 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{23}+\left(\left\{\begin{array}{cc}-6 & n =0 \\ -1 & n =1 \\ 2 & n =2 \\ 1 & n =3 \\ 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) = 19
a(5) = 49
a(6) = 116
a(7) = 271
a(n+3) = a(n)-2*a(n+1)+3*a(n+2)+2, n >= 8
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) = 49
a \! \left(6\right) = 116
a \! \left(7\right) = 271
a \! \left(n +3\right) = a \! \left(n \right)-2 a \! \left(n +1\right)+3 a \! \left(n +2\right)+2, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17209/
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[25,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[14,x]+F[24,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[4,x]
F[23,x] = F[19,x]
F[24,x] = F[20,x]
F[25,x] = F[26,x]+F[52,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[1,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[17,x]*F[4,x]
F[32,x] = F[26,x]+F[33,x]
F[33,x] = F[34,x]+F[35,x]+F[50,x]
F[34,x] = 0
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[30,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[22,x]*F[4,x]
F[40,x] = F[33,x]+F[41,x]
F[41,x] = 2*F[34,x]+F[42,x]+F[46,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[38,x]
F[45,x] = F[41,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[26,x]*F[4,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[26,x]+F[48,x]
F[52,x] = F[34,x]+F[53,x]+F[77,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[63,x]
F[55,x] = F[30,x]+F[56,x]
F[56,x] = F[34,x]+F[57,x]+F[61,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[4,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = x^2
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[30,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[34,x]+F[50,x]+F[53,x]
F[65,x] = F[34,x]+F[66,x]+F[71,x]+F[75,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[38,x]
F[69,x] = F[70,x]
F[70,x] = 2*F[34,x]+F[46,x]+F[66,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[48,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[48,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[33,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[26,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[4,x]*F[79,x]
F[82,x] = F[83,x]+F[91,x]
F[83,x] = F[34,x]+F[35,x]+F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[51,x]+F[86,x]
F[86,x] = F[83,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[47,x]+F[90,x]
F[90,x] = F[87,x]
F[91,x] = F[88,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_{25}\! \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_{14}\! \left(x \right)+F_{24}\! \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_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{20}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{52}\! \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_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{50}\! \left(x \right)
F_{34}\! \left(x \right) = 0
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{30}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{33}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{38}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{26}\! \left(x \right)+F_{48}\! \left(x \right)
F_{52}\! \left(x \right) = F_{34}\! \left(x \right)+F_{53}\! \left(x \right)+F_{77}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{63}\! \left(x \right)
F_{55}\! \left(x \right) = F_{30}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{34}\! \left(x \right)+F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \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_{60}\! \left(x \right)
F_{60}\! \left(x \right) = x^{2}
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{30}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{34}\! \left(x \right)+F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{65}\! \left(x \right) = F_{34}\! \left(x \right)+F_{66}\! \left(x \right)+F_{71}\! \left(x \right)+F_{75}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{38}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{46}\! \left(x \right)+F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{48}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{33}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{26}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{91}\! \left(x \right)
F_{83}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{51}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{83}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{47}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{87}\! \left(x \right)
F_{91}\! \left(x \right) = F_{88}\! \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_25(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_14(x) + F_24(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_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_4(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_20(x))
Eq(F_25(x), F_26(x) + F_52(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_1(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_17(x)*F_4(x))
Eq(F_32(x), F_26(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_50(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_30(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_22(x)*F_4(x))
Eq(F_40(x), F_33(x) + F_41(x))
Eq(F_41(x), 2*F_34(x) + F_42(x) + F_46(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_38(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_26(x)*F_4(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_26(x) + F_48(x))
Eq(F_52(x), F_34(x) + F_53(x) + F_77(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_63(x))
Eq(F_55(x), F_30(x) + F_56(x))
Eq(F_56(x), F_34(x) + F_57(x) + F_61(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_4(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), x**2)
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_30(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_34(x) + F_50(x) + F_53(x))
Eq(F_65(x), F_34(x) + F_66(x) + F_71(x) + F_75(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_38(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), 2*F_34(x) + F_46(x) + F_66(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_48(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_48(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_33(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_26(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_4(x)*F_79(x))
Eq(F_82(x), F_83(x) + F_91(x))
Eq(F_83(x), F_34(x) + F_35(x) + F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_51(x) + F_86(x))
Eq(F_86(x), F_83(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_47(x) + F_90(x))
Eq(F_90(x), F_87(x))
Eq(F_91(x), F_88(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:
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1], "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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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": 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