0132_1023_1230_3021
Counting sequence:
1, 1, 2, 6, 20, 59, 151, 357, 802, 1742, 3698, 7727, 15967, 32733, 66718, 135410, 273950, 552887, 1113751, 2240301, 4501186, 9035534, 18124562, 36335495, 72810535, 145846629, 292057966, 584705762, 1170365582, 2342274527, 4687045903, 9378131397, 18762798562, 37536171758, 75089453138, 150206589695, 300457971535, 600988417677, 1202094101086, 2404377941426, 4809062886686, 9618622515239, 19238048774887, 38477398034685, 76956900297250, 153917205305774, 307839919549106, 615688752745367, 1231391928073687, 2462807192375637, 4925652143560558, 9851365382156642, 19702829618155982, 39405819185187983, 78811897173092383, 157624213097774805, 315249103749853570, 630499303805598542, 1261000381471389746, 2522003633108860751, 5044011910243992511, 10088031334680334269, 20176074827579285662, 40352169327569534450, 80704370485768645790, 161408792474577828119, 322817668282825766071, 645635471402362174797, 1291271160975105098242, 2582542674957301583822, 5165085921092075299538, 10330172766368714114087, 20660347028099463870727, 41320696475745526894533, 82641396866399688580078, 165282800067254611099490, 330565610383873090924430, 661131237351565284508607, 1322262501536313540397231, 2644525046489629154828901, 5289050163229443355066786, 10578100440126073829571374, 21156201064169519823983762, 42312402425923598932240415, 84624805333349129313588655, 169249611445784749360551789, 338499224152157920903579486, 676998450343990754723002802, 1353996903988244844544318622, 2707993813316427937102787207, 5415987635273057457318030343, 10831975284526254745762659357, 21663950591672850905764365922, 43327901219946183056894370158, 86655802499113188773393418098, 173311605094047681451757144375, 346623210343137489468089266615, 693246420937138409405723810997, 1386492842280182375845567869166, 2772985685217133739194801254626, 5545971371496942022927388263886
Generating function in Maple syntax:
(2*x^9-6*x^7+6*x^6+x^4+4*x^3-9*x^2+5*x-1)/(2*x-1)/(x^2+x-1)/(x-1)^3
Generating function in latex syntax:
\frac{2 x^{9}-6 x^{7}+6 x^{6}+x^{4}+4 x^{3}-9 x^{2}+5 x -1}{\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(2*x**9 - 6*x**7 + 6*x**6 + x**4 + 4*x**3 - 9*x**2 + 5*x - 1)/((x - 1)**3*(2*x - 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2+x-1)*(x-1)^3*F(x)+2*x^9-6*x^7+6*x^6+x^4+4*x^3-9*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+2 x^{9}-6 x^{7}+6 x^{6}+x^{4}+4 x^{3}-9 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
-n^2+piecewise(n = 0,45/8,n = 1,13/4,n = 2,5/2,n = 3,1,0)+2*n-3+6/5*(-1/2*5^(1/2)-1/2)^(-n)*5^(1/2)-6/5*(1/2*5^(1/2)-1/2)^(-n)*5^(1/2)+35/8*2^n-3*(-1/2*5^(1/2)-1/2)^(-n)-3*(1/2*5^(1/2)-1/2)^(-n)
Explicit closed form in latex syntax:
-n^{2}+\left(\left\{\begin{array}{cc}\frac{45}{8} & n =0 \\ \frac{13}{4} & n =1 \\ \frac{5}{2} & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+2 n -3+\frac{6 \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n} \sqrt{5}}{5}-\frac{6 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n} \sqrt{5}}{5}+\frac{35 \,2^{n}}{8}-3 \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}-3 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 59
a(6) = 151
a(7) = 357
a(8) = 802
a(9) = 1742
a(n+3) = -2*a(n)-a(n+1)+3*a(n+2)-(-1+n)*(n-5), n >= 10
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(5\right) = 59
a \! \left(6\right) = 151
a \! \left(7\right) = 357
a \! \left(8\right) = 802
a \! \left(9\right) = 1742
a \! \left(n +3\right) = -2 a \! \left(n \right)-a \! \left(n +1\right)+3 a \! \left(n +2\right)-\left(-1+n \right) \left(n -5\right), \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15480/
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[35,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[7,x]
F[14,x] = F[15,x]+F[16,x]+F[32,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]+F[4,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[4,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[15,x]+F[16,x]+F[23,x]
F[23,x] = F[4,x]*F[7,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[18,x]+F[30,x]
F[30,x] = F[27,x]+F[31,x]
F[31,x] = F[25,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[7,x]
F[34,x] = F[28,x]
F[35,x] = F[36,x]+F[7,x]
F[36,x] = F[15,x]+F[37,x]+F[74,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[46,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[1,x]+F[40,x]
F[43,x] = F[15,x]+F[20,x]+F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[11,x]+F[43,x]
F[46,x] = F[47,x]+F[51,x]
F[47,x] = F[15,x]+F[37,x]+F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[7,x]
F[50,x] = F[15,x]+F[16,x]+F[48,x]
F[51,x] = F[15,x]+F[25,x]+F[52,x]+F[70,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[61,x]
F[54,x] = F[55,x]+F[58,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[4,x]+F[55,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[19,x]+F[58,x]
F[61,x] = F[62,x]+F[66,x]
F[62,x] = 2*F[15,x]+F[52,x]+F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[22,x]+F[65,x]
F[65,x] = F[63,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[24,x]+F[69,x]
F[69,x] = F[67,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[14,x]+F[72,x]
F[72,x] = F[15,x]+F[25,x]+F[70,x]+F[73,x]
F[73,x] = 0
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[33,x]+F[76,x]
F[76,x] = F[77,x]+F[85,x]
F[77,x] = F[15,x]+F[16,x]+F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[33,x]+F[80,x]
F[80,x] = F[77,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[26,x]+F[84,x]
F[84,x] = F[82,x]
F[85,x] = 2*F[15,x]+F[86,x]+F[91,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[90,x]
F[88,x] = F[89,x]
F[89,x] = x^2
F[90,x] = F[86,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[26,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = 2*F[15,x]+F[86,x]+F[91,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_{35}\! \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_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{32}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \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_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{28}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{7}\! \left(x \right)
F_{36}\! \left(x \right) = F_{15}\! \left(x \right)+F_{37}\! \left(x \right)+F_{74}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{46}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{47}\! \left(x \right) = F_{15}\! \left(x \right)+F_{37}\! \left(x \right)+F_{48}\! \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_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{52}\! \left(x \right)+F_{70}\! \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_{61}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \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_{4}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{19}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{52}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{22}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{24}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{14}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 0
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{33}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{77}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{33}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{77}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{26}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{86}\! \left(x \right)+F_{91}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = x^{2}
F_{90}\! \left(x \right) = F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{26}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{86}\! \left(x \right)+F_{91}\! \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_35(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_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_32(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x) + F_4(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_15(x) + F_16(x) + F_23(x))
Eq(F_23(x), F_4(x)*F_7(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_18(x) + F_30(x))
Eq(F_30(x), F_27(x) + F_31(x))
Eq(F_31(x), F_25(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_7(x))
Eq(F_34(x), F_28(x))
Eq(F_35(x), F_36(x) + F_7(x))
Eq(F_36(x), F_15(x) + F_37(x) + F_74(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_46(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_1(x) + F_40(x))
Eq(F_43(x), F_15(x) + F_20(x) + F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_11(x) + F_43(x))
Eq(F_46(x), F_47(x) + F_51(x))
Eq(F_47(x), F_15(x) + F_37(x) + F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_7(x))
Eq(F_50(x), F_15(x) + F_16(x) + F_48(x))
Eq(F_51(x), F_15(x) + F_25(x) + F_52(x) + F_70(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_61(x))
Eq(F_54(x), F_55(x) + F_58(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_4(x) + F_55(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_19(x) + F_58(x))
Eq(F_61(x), F_62(x) + F_66(x))
Eq(F_62(x), 2*F_15(x) + F_52(x) + F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_22(x) + F_65(x))
Eq(F_65(x), F_63(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_24(x) + F_69(x))
Eq(F_69(x), F_67(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_14(x) + F_72(x))
Eq(F_72(x), F_15(x) + F_25(x) + F_70(x) + F_73(x))
Eq(F_73(x), 0)
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_33(x) + F_76(x))
Eq(F_76(x), F_77(x) + F_85(x))
Eq(F_77(x), F_15(x) + F_16(x) + F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_33(x) + F_80(x))
Eq(F_80(x), F_77(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_26(x) + F_84(x))
Eq(F_84(x), F_82(x))
Eq(F_85(x), 2*F_15(x) + F_86(x) + F_91(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_90(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), x**2)
Eq(F_90(x), F_86(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_26(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), 2*F_15(x) + F_86(x) + F_91(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, 0], [1, 2], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], 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