0132_0231_0321_1032_3120
Counting sequence:
1, 1, 2, 6, 19, 56, 152, 388, 948, 2245, 5195, 11810, 26474, 58675, 128829, 280648, 607316, 1306721, 2797679, 5963902, 12664974, 26804383, 56557745, 119013572, 249823448, 523239661, 1093665027, 2281701658, 4752146738, 9881780555, 20518535525, 42547020160, 88113938844, 182267675065, 376614945239, 777389081078, 1603096543766, 3302829851191, 6798933230169, 13984413516412, 28741921145504, 59030030516933, 121152437486315, 248489627878162, 509348761568058, 1043436534760291, 2136351092769677, 4371658232038328, 8941228557075428, 18278281300149265, 37348210972296255, 76279718688588910, 155726030865171614, 317785248706331855, 648236871364642049, 1321806490633241908, 2694278477074400616, 5489887945764636061, 11182437874760943059, 22770199715985229322, 46351047364897146434, 94323390595647669883, 191889372923002095285, 390263929309417703152, 793498225545662433068, 1612937184944978921321, 3277755837597265954727, 6659274610609148135398, 13526075092047528724518, 27467201925753522358375, 55764507334823974537385, 113189221636281808718060, 229698857205831336724784, 466038542278198112029045, 945358740289467101219259, 1917280792045075956763138, 3887688207022435422177866, 7881629659909437861661331, 15975765811548009757936349, 32376544606554287585102632, 65603115180025111308667764, 132906282293883294894263233, 269212668455432734342384655, 545225544646197757792488542, 1104051504763060093800418478, 2235303840467449344031722751, 4525009342817557000925220177, 9158822009400430627573992868, 18535250666331494506595094008, 37505714627724255516084407885, 75881855845571044037957258915, 153504564871387154087491407610, 310490836103264440198136598354, 627945084927509144442580766635, 1269816995296978816977776676869, 2567487641477878690140783644768, 5190682584723599492652027875516, 10492779772982883210044976927001, 21208388753037134869571796210039, 42862435920217006638107277136342, 86616188668719487074141923709494
Generating function in Maple syntax:
-(x^9+x^7-x^6-x^5+6*x^4-14*x^3+14*x^2-6*x+1)/(x-1)^3/(2*x-1)^2
Generating function in latex syntax:
-\frac{x^{9}+x^{7}-x^{6}-x^{5}+6 x^{4}-14 x^{3}+14 x^{2}-6 x +1}{\left(x -1\right)^{3} \left(2 x -1\right)^{2}}
Generating function in sympy syntax:
(-x**9 - x**7 + x**6 + x**5 - 6*x**4 + 14*x**3 - 14*x**2 + 6*x - 1)/((x - 1)**3*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(x-1)^3*(2*x-1)^2*F(x)+x^9+x^7-x^6-x^5+6*x^4-14*x^3+14*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right)^{3} \left(2 x -1\right)^{2} F \! \left(x \right)+x^{9}+x^{7}-x^{6}-x^{5}+6 x^{4}-14 x^{3}+14 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,n = 3,6,n = 4,19,1/64*(45*n-127)*2^n+1/2*n^2-7/2*n+12)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 6 & n =3 \\ 19 & n =4 \\ \frac{\left(45 n -127\right) 2^{n}}{64}+\frac{n^{2}}{2}-\frac{7 n}{2}+12 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 152
a(7) = 388
a(8) = 948
a(9) = 2245
a(n+2) = 1/2*n^2-4*a(n)+4*a(n+1)-11/2*n+19, 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) = 19
a \! \left(5\right) = 56
a \! \left(6\right) = 152
a \! \left(7\right) = 388
a \! \left(8\right) = 948
a \! \left(9\right) = 2245
a \! \left(n +2\right) = \frac{n^{2}}{2}-4 a \! \left(n \right)+4 a \! \left(n +1\right)-\frac{11 n}{2}+19, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21673/
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[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[19,x]*F[7,x]
F[7,x] = F[120,x]+F[8,x]
F[8,x] = F[65,x]+F[9,x]
F[9,x] = F[10,x]+F[23,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[19,x]
F[13,x] = F[10,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[19,x]*F[20,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]*F[19,x]
F[19,x] = x
F[20,x] = F[10,x]+F[21,x]
F[21,x] = F[19,x]*F[22,x]
F[22,x] = F[1,x]+F[21,x]
F[23,x] = F[19,x]+F[24,x]
F[24,x] = F[25,x]+F[26,x]+F[28,x]
F[25,x] = 0
F[26,x] = F[19,x]*F[27,x]
F[27,x] = F[21,x]
F[28,x] = F[19,x]*F[29,x]
F[29,x] = F[30,x]+F[46,x]
F[30,x] = F[19,x]+F[31,x]
F[31,x] = F[25,x]+F[26,x]+F[32,x]
F[32,x] = F[19,x]*F[33,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[19,x]+F[35,x]
F[35,x] = F[25,x]+F[26,x]+F[36,x]
F[36,x] = F[19,x]*F[34,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[25,x]+F[39,x]+F[40,x]
F[39,x] = x^2
F[40,x] = x^2
F[41,x] = F[25,x]+F[42,x]+F[44,x]+F[45,x]
F[42,x] = F[19,x]*F[43,x]
F[43,x] = F[26,x]
F[44,x] = F[19,x]*F[35,x]
F[45,x] = F[19,x]*F[37,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[25,x]+F[39,x]+F[48,x]
F[48,x] = F[19,x]*F[49,x]
F[49,x] = F[19,x]+F[47,x]
F[50,x] = F[25,x]+F[42,x]+F[51,x]+F[56,x]
F[51,x] = F[19,x]*F[52,x]
F[52,x] = F[35,x]+F[53,x]
F[53,x] = F[25,x]+F[42,x]+F[51,x]+F[54,x]
F[54,x] = F[19,x]*F[55,x]
F[55,x] = F[47,x]+F[53,x]
F[56,x] = F[19,x]*F[57,x]
F[57,x] = F[55,x]+F[58,x]
F[58,x] = F[59,x]+F[61,x]
F[59,x] = F[60,x]
F[60,x] = F[19,x]*F[47,x]
F[61,x] = 2*F[25,x]+F[62,x]+F[63,x]+F[64,x]
F[62,x] = 0
F[63,x] = F[19,x]*F[53,x]
F[64,x] = F[19,x]*F[58,x]
F[65,x] = F[66,x]*F[89,x]
F[66,x] = F[67,x]
F[67,x] = F[19,x]*F[68,x]
F[68,x] = F[69,x]+F[75,x]
F[69,x] = F[1,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[19,x]*F[72,x]
F[72,x] = F[22,x]+F[73,x]
F[73,x] = F[19,x]+F[74,x]
F[74,x] = F[26,x]
F[75,x] = F[17,x]+F[76,x]
F[76,x] = F[25,x]+F[77,x]+F[82,x]
F[77,x] = F[19,x]*F[78,x]
F[78,x] = F[27,x]+F[79,x]
F[79,x] = F[25,x]+F[77,x]+F[80,x]
F[80,x] = F[19,x]*F[81,x]
F[81,x] = F[17,x]+F[79,x]
F[82,x] = F[19,x]*F[83,x]
F[83,x] = F[81,x]+F[84,x]
F[84,x] = F[85,x]+F[87,x]
F[85,x] = F[86,x]
F[86,x] = F[17,x]*F[19,x]
F[87,x] = F[88,x]
F[88,x] = F[19,x]*F[79,x]
F[89,x] = F[10,x]+F[90,x]
F[90,x] = F[19,x]+F[91,x]
F[91,x] = F[25,x]+F[26,x]+F[92,x]
F[92,x] = F[19,x]*F[93,x]
F[93,x] = F[102,x]+F[94,x]
F[94,x] = F[19,x]+F[95,x]
F[95,x] = F[25,x]+F[26,x]+F[96,x]
F[96,x] = F[19,x]*F[97,x]
F[97,x] = F[34,x]+F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[40,x]
F[100,x] = 2*F[25,x]+F[101,x]+F[44,x]
F[101,x] = F[19,x]*F[98,x]
F[102,x] = F[103,x]+F[106,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[19,x]
F[105,x] = F[103,x]+F[19,x]
F[106,x] = 2*F[25,x]+F[107,x]+F[112,x]
F[107,x] = F[108,x]*F[19,x]
F[108,x] = F[109,x]+F[35,x]
F[109,x] = 2*F[25,x]+F[107,x]+F[110,x]
F[110,x] = F[111,x]*F[19,x]
F[111,x] = F[103,x]+F[109,x]
F[112,x] = F[113,x]*F[19,x]
F[113,x] = F[111,x]+F[114,x]
F[114,x] = F[115,x]+F[117,x]
F[115,x] = F[116,x]
F[116,x] = F[103,x]*F[19,x]
F[117,x] = 3*F[25,x]+F[118,x]+F[119,x]
F[118,x] = F[109,x]*F[19,x]
F[119,x] = F[114,x]*F[19,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[20,x]
F[122,x] = F[39,x]+F[66,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_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{120}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{65}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \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_{19}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \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_{19}\! \left(x \right) F_{20}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{19}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{21}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{46}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{19}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{19}\! \left(x \right) F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{25}\! \left(x \right)+F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = x^{2}
F_{40}\! \left(x \right) = x^{2}
F_{41}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{19}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{26}\! \left(x \right)
F_{44}\! \left(x \right) = F_{19}\! \left(x \right) F_{35}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right) F_{37}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{25}\! \left(x \right)+F_{39}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{19}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{19}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)+F_{51}\! \left(x \right)+F_{56}\! \left(x \right)
F_{51}\! \left(x \right) = F_{19}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{35}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)+F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{19}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{62}\! \left(x \right) = 0
F_{63}\! \left(x \right) = F_{19}\! \left(x \right) F_{53}\! \left(x \right)
F_{64}\! \left(x \right) = F_{19}\! \left(x \right) F_{58}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right) F_{89}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{19}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{69}\! \left(x \right) = F_{1}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{19}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{22}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{19}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{26}\! \left(x \right)
F_{75}\! \left(x \right) = F_{17}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{25}\! \left(x \right)+F_{77}\! \left(x \right)+F_{82}\! \left(x \right)
F_{77}\! \left(x \right) = F_{19}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{27}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{25}\! \left(x \right)+F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{17}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{19}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{19}\! \left(x \right) F_{79}\! \left(x \right)
F_{89}\! \left(x \right) = F_{10}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{19}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{19}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{102}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{19}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{19}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{34}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{40}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{101}\! \left(x \right)+F_{44}\! \left(x \right)
F_{101}\! \left(x \right) = F_{19}\! \left(x \right) F_{98}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{106}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{19}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{19}\! \left(x \right)
F_{106}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{107}\! \left(x \right)+F_{112}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{19}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{35}\! \left(x \right)
F_{109}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{107}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{19}\! \left(x \right)
F_{111}\! \left(x \right) = F_{103}\! \left(x \right)+F_{109}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{19}\! \left(x \right)
F_{113}\! \left(x \right) = F_{111}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{103}\! \left(x \right) F_{19}\! \left(x \right)
F_{117}\! \left(x \right) = 3 F_{25}\! \left(x \right)+F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{109}\! \left(x \right) F_{19}\! \left(x \right)
F_{119}\! \left(x \right) = F_{114}\! \left(x \right) F_{19}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{20}\! \left(x \right)
F_{122}\! \left(x \right) = F_{39}\! \left(x \right)+F_{66}\! \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_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_19(x)*F_7(x))
Eq(F_7(x), F_120(x) + F_8(x))
Eq(F_8(x), F_65(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_23(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_19(x))
Eq(F_13(x), F_10(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_19(x)*F_20(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_16(x)*F_19(x))
Eq(F_19(x), x)
Eq(F_20(x), F_10(x) + F_21(x))
Eq(F_21(x), F_19(x)*F_22(x))
Eq(F_22(x), F_1(x) + F_21(x))
Eq(F_23(x), F_19(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_28(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_19(x)*F_27(x))
Eq(F_27(x), F_21(x))
Eq(F_28(x), F_19(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_46(x))
Eq(F_30(x), F_19(x) + F_31(x))
Eq(F_31(x), F_25(x) + F_26(x) + F_32(x))
Eq(F_32(x), F_19(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_19(x) + F_35(x))
Eq(F_35(x), F_25(x) + F_26(x) + F_36(x))
Eq(F_36(x), F_19(x)*F_34(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_25(x) + F_39(x) + F_40(x))
Eq(F_39(x), x**2)
Eq(F_40(x), x**2)
Eq(F_41(x), F_25(x) + F_42(x) + F_44(x) + F_45(x))
Eq(F_42(x), F_19(x)*F_43(x))
Eq(F_43(x), F_26(x))
Eq(F_44(x), F_19(x)*F_35(x))
Eq(F_45(x), F_19(x)*F_37(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_25(x) + F_39(x) + F_48(x))
Eq(F_48(x), F_19(x)*F_49(x))
Eq(F_49(x), F_19(x) + F_47(x))
Eq(F_50(x), F_25(x) + F_42(x) + F_51(x) + F_56(x))
Eq(F_51(x), F_19(x)*F_52(x))
Eq(F_52(x), F_35(x) + F_53(x))
Eq(F_53(x), F_25(x) + F_42(x) + F_51(x) + F_54(x))
Eq(F_54(x), F_19(x)*F_55(x))
Eq(F_55(x), F_47(x) + F_53(x))
Eq(F_56(x), F_19(x)*F_57(x))
Eq(F_57(x), F_55(x) + F_58(x))
Eq(F_58(x), F_59(x) + F_61(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_19(x)*F_47(x))
Eq(F_61(x), 2*F_25(x) + F_62(x) + F_63(x) + F_64(x))
Eq(F_62(x), 0)
Eq(F_63(x), F_19(x)*F_53(x))
Eq(F_64(x), F_19(x)*F_58(x))
Eq(F_65(x), F_66(x)*F_89(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_19(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_75(x))
Eq(F_69(x), F_1(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_19(x)*F_72(x))
Eq(F_72(x), F_22(x) + F_73(x))
Eq(F_73(x), F_19(x) + F_74(x))
Eq(F_74(x), F_26(x))
Eq(F_75(x), F_17(x) + F_76(x))
Eq(F_76(x), F_25(x) + F_77(x) + F_82(x))
Eq(F_77(x), F_19(x)*F_78(x))
Eq(F_78(x), F_27(x) + F_79(x))
Eq(F_79(x), F_25(x) + F_77(x) + F_80(x))
Eq(F_80(x), F_19(x)*F_81(x))
Eq(F_81(x), F_17(x) + F_79(x))
Eq(F_82(x), F_19(x)*F_83(x))
Eq(F_83(x), F_81(x) + F_84(x))
Eq(F_84(x), F_85(x) + F_87(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_17(x)*F_19(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_19(x)*F_79(x))
Eq(F_89(x), F_10(x) + F_90(x))
Eq(F_90(x), F_19(x) + F_91(x))
Eq(F_91(x), F_25(x) + F_26(x) + F_92(x))
Eq(F_92(x), F_19(x)*F_93(x))
Eq(F_93(x), F_102(x) + F_94(x))
Eq(F_94(x), F_19(x) + F_95(x))
Eq(F_95(x), F_25(x) + F_26(x) + F_96(x))
Eq(F_96(x), F_19(x)*F_97(x))
Eq(F_97(x), F_34(x) + F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_40(x))
Eq(F_100(x), F_101(x) + 2*F_25(x) + F_44(x))
Eq(F_101(x), F_19(x)*F_98(x))
Eq(F_102(x), F_103(x) + F_106(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_19(x))
Eq(F_105(x), F_103(x) + F_19(x))
Eq(F_106(x), F_107(x) + F_112(x) + 2*F_25(x))
Eq(F_107(x), F_108(x)*F_19(x))
Eq(F_108(x), F_109(x) + F_35(x))
Eq(F_109(x), F_107(x) + F_110(x) + 2*F_25(x))
Eq(F_110(x), F_111(x)*F_19(x))
Eq(F_111(x), F_103(x) + F_109(x))
Eq(F_112(x), F_113(x)*F_19(x))
Eq(F_113(x), F_111(x) + F_114(x))
Eq(F_114(x), F_115(x) + F_117(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_103(x)*F_19(x))
Eq(F_117(x), F_118(x) + F_119(x) + 3*F_25(x))
Eq(F_118(x), F_109(x)*F_19(x))
Eq(F_119(x), F_114(x)*F_19(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_20(x))
Eq(F_122(x), F_39(x) + F_66(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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "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, 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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "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": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}], "requirements": []}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 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