0123_0132_1023_1320_3021

Counting sequence:
1, 1, 2, 6, 19, 50, 115, 257, 577, 1306, 2984, 6881, 16001, 37481, 88337, 209250, 497686, 1187547, 2840879, 6809573, 16347849, 39293854, 94535508, 227604649, 548293765, 1321410293, 3185757857, 7682569118, 18530792026, 44704985835, 107864200891, 260283271049, 628135608529, 1515972841090, 3658932549248, 8831564977361, 21317557831049, 51457740590369, 124215275164721, 299852958000954, 723850851285598, 1747414525699803, 4218400542875015, 10183658409899597, 24584605489912473, 59350649858190022, 143281473155465388, 345904743727191769, 835073275099366669, 2016015955072964717, 4867034560917067073, 11749943916767551670, 28366640220875205538, 68482660254361815339, 165330832923572722195, 399142071155104005809, 963610466441860660897, 2326353988274836881898, 5616300414470563239512, 13558918765140462259265, 32734065848799783963281, 79026906284367797569625, 190787590083112673981777, 460601509818557392402578, 1111989456516835378504102, 2684578116545437802716251, 6481141077158856269934815, 15646851046236718178160437, 37774824720826041750227817, 91196463591011358323138926, 220167678110303321424988164, 531531672228516580936308361, 1283230727404405269729904021, 3097992536716843442903316581, 7479214620205965569590161377, 18056419415879048990393883470, 43592048729488479170252515306, 105240507429944039469638231787, 254073044699616995058796785259, 613386559049764588541624707673, 1480846087240492764233101381489, 3575078582413727988367765379794, 8631002949834371589442928668208, 20837083877616083129468488702769, 50305169496135018560558680155545, 121447420452025142617021085362193, 293200005564466727563088775481457, 707847421909526984452722720373098, 1708894830040666548596391887440366, 4125637043305166663478076486763355, 9960168839279637415699489723676471, 24045974567121756509121242826921629, 58052117664037845872950229576309049, 140150209276226946257487803962397590, 338352534978550909807894709836093788, 816855276757447395912747840634647481, 1972063083541683431867014970551216669, 4760981433937290489668403573526399709, 11494025931609218130696407899394243201, 27749033257541636250990536401994692454, 66992092367464313004610303281912505138

Generating function in Maple syntax:
-(2*x^14+9*x^13+x^12-37*x^11-22*x^10+50*x^9+29*x^8-24*x^7-15*x^6-10*x^5+15*x^4+11*x^3-17*x^2+7*x-1)/(2*x-1)/(x^2+2*x-1)/(x-1)^2/(x^2+x-1)^2

Generating function in latex syntax:
-\frac{2 x^{14}+9 x^{13}+x^{12}-37 x^{11}-22 x^{10}+50 x^{9}+29 x^{8}-24 x^{7}-15 x^{6}-10 x^{5}+15 x^{4}+11 x^{3}-17 x^{2}+7 x -1}{\left(2 x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{2} \left(x^{2}+x -1\right)^{2}}

Generating function in sympy syntax:
(-2*x**14 - 9*x**13 - x**12 + 37*x**11 + 22*x**10 - 50*x**9 - 29*x**8 + 24*x**7 + 15*x**6 + 10*x**5 - 15*x**4 - 11*x**3 + 17*x**2 - 7*x + 1)/((x - 1)**2*(2*x - 1)*(x**2 + x - 1)**2*(x**2 + 2*x - 1))

Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2+2*x-1)*(x-1)^2*(x^2+x-1)^2*F(x)+2*x^14+9*x^13+x^12-37*x^11-22*x^10+50*x^9+29*x^8-24*x^7-15*x^6-10*x^5+15*x^4+11*x^3-17*x^2+7*x-1 = 0

Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{2} \left(x^{2}+x -1\right)^{2} F \! \left(x \right)+2 x^{14}+9 x^{13}+x^{12}-37 x^{11}-22 x^{10}+50 x^{9}+29 x^{8}-24 x^{7}-15 x^{6}-10 x^{5}+15 x^{4}+11 x^{3}-17 x^{2}+7 x -1 = 0

Explicit closed form in Maple syntax:
-piecewise(n = 0,-15/4,n = 1,-7/2,n = 3,2,n = 4,3,n = 5,1,0)+1/100*((-10*n+42)*5^(1/2)+10*n+50)*(-1/2*5^(1/2)-1/2)^(-n)+1/100*((10*n-42)*5^(1/2)+10*n+50)*(1/2*5^(1/2)-1/2)^(-n)-1/4*(-1-2^(1/2))^(-n)*2^(1/2)+1/4*(2^(1/2)-1)^(-n)*2^(1/2)+n+1/4*2^n-4

Explicit closed form in latex syntax:
-\left(\left\{\begin{array}{cc}-\frac{15}{4} & n =0 \\ -\frac{7}{2} & n =1 \\ 2 & n =3 \\ 3 & n =4 \\ 1 & n =5 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(\left(-10 n +42\right) \sqrt{5}+10 n +50\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{100}+\frac{\left(\left(10 n -42\right) \sqrt{5}+10 n +50\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{100}-\frac{\left(-1-\sqrt{2}\right)^{-n} \sqrt{2}}{4}+\frac{\left(\sqrt{2}-1\right)^{-n} \sqrt{2}}{4}+n +\frac{2^{n}}{4}-4

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 50
a(6) = 115
a(7) = 257
a(8) = 577
a(9) = 1306
a(10) = 2984
a(11) = 6881
a(12) = 16001
a(13) = 37481
a(14) = 88337
a(n+1) = -2/7*a(n)+2*a(n+3)-2/7*a(n+4)-10/7*a(n+5)+6/7*a(n+6)-1/7*a(n+7)+2/7*n-2, n >= 15

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) = 50
a \! \left(6\right) = 115
a \! \left(7\right) = 257
a \! \left(8\right) = 577
a \! \left(9\right) = 1306
a \! \left(10\right) = 2984
a \! \left(11\right) = 6881
a \! \left(12\right) = 16001
a \! \left(13\right) = 37481
a \! \left(14\right) = 88337
a \! \left(n +1\right) = -\frac{2 a \! \left(n \right)}{7}+2 a \! \left(n +3\right)-\frac{2 a \! \left(n +4\right)}{7}-\frac{10 a \! \left(n +5\right)}{7}+\frac{6 a \! \left(n +6\right)}{7}-\frac{a \! \left(n +7\right)}{7}+\frac{2 n}{7}-2, \quad n \geq 15

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16321/
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[19,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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]+F[14,x]+F[18,x]
F[13,x] = 0
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[4,x]
F[17,x] = F[12,x]
F[18,x] = F[4,x]*F[7,x]
F[19,x] = F[20,x]+F[41,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[10,x]*F[4,x]
F[26,x] = F[20,x]+F[27,x]
F[27,x] = F[13,x]+F[28,x]+F[39,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[31,x]+F[4,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[4,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[13,x]+F[28,x]+F[35,x]
F[35,x] = F[20,x]*F[4,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[34,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[20,x]+F[34,x]
F[41,x] = F[102,x]+F[13,x]+F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[52,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[1,x]+F[45,x]
F[48,x] = F[13,x]+F[32,x]+F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[24,x]+F[51,x]
F[51,x] = F[32,x]
F[52,x] = F[53,x]+F[64,x]
F[53,x] = F[13,x]+F[42,x]+F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[20,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[30,x]+F[59,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[57,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[60,x]
F[64,x] = F[100,x]+F[13,x]+F[65,x]+F[78,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[74,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[4,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[31,x]
F[74,x] = F[75,x]
F[75,x] = 2*F[13,x]+F[65,x]+F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[60,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[13,x]+F[35,x]+F[81,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[4,x]+F[84,x]
F[84,x] = F[13,x]+F[32,x]+F[85,x]
F[85,x] = F[24,x]*F[4,x]
F[86,x] = F[80,x]+F[87,x]
F[87,x] = F[13,x]+F[78,x]+F[88,x]+F[98,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[95,x]
F[90,x] = F[91,x]+F[93,x]
F[91,x] = F[92,x]
F[92,x] = x^2
F[93,x] = F[94,x]
F[94,x] = F[31,x]*F[4,x]
F[95,x] = F[96,x]
F[96,x] = 2*F[13,x]+F[88,x]+F[97,x]
F[97,x] = F[4,x]*F[60,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[57,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[99,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[20,x]+F[80,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[57,x]
F[107,x] = 2*F[13,x]+F[108,x]+F[112,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[90,x]
F[110,x] = F[111,x]
F[111,x] = 2*F[13,x]+F[108,x]+F[97,x]
F[112,x] = F[106,x]*F[4,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_{19}\! \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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = 0
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
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_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{13}\! \left(x \right)+F_{28}\! \left(x \right)+F_{39}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right)+F_{28}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)
F_{41}\! \left(x \right) = F_{102}\! \left(x \right)+F_{13}\! \left(x \right)+F_{42}\! \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_{52}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{48}\! \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_{1}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{24}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{32}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{64}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13}\! \left(x \right)+F_{42}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{30}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{57}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{60}\! \left(x \right)
F_{64}\! \left(x \right) = F_{100}\! \left(x \right)+F_{13}\! \left(x \right)+F_{65}\! \left(x \right)+F_{78}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{74}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \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_{4}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{31}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{65}\! \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_{60}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{13}\! \left(x \right)+F_{35}\! \left(x \right)+F_{81}\! \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_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{86}\! \left(x \right) = F_{80}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{13}\! \left(x \right)+F_{78}\! \left(x \right)+F_{88}\! \left(x \right)+F_{98}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{95}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{93}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = x^{2}
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{88}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{57}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{99}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{20}\! \left(x \right)+F_{80}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{57}\! \left(x \right)
F_{107}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{90}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{108}\! \left(x \right)+F_{97}\! \left(x \right)
F_{112}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \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_19(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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x) + F_14(x) + F_18(x))
Eq(F_13(x), 0)
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_4(x))
Eq(F_17(x), F_12(x))
Eq(F_18(x), F_4(x)*F_7(x))
Eq(F_19(x), F_20(x) + F_41(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_10(x)*F_4(x))
Eq(F_26(x), F_20(x) + F_27(x))
Eq(F_27(x), F_13(x) + F_28(x) + F_39(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_31(x) + F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_13(x) + F_28(x) + F_35(x))
Eq(F_35(x), F_20(x)*F_4(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_34(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_20(x) + F_34(x))
Eq(F_41(x), F_102(x) + F_13(x) + F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_52(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_1(x) + F_45(x))
Eq(F_48(x), F_13(x) + F_32(x) + F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_24(x) + F_51(x))
Eq(F_51(x), F_32(x))
Eq(F_52(x), F_53(x) + F_64(x))
Eq(F_53(x), F_13(x) + F_42(x) + F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_20(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_30(x) + F_59(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_57(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_60(x))
Eq(F_64(x), F_100(x) + F_13(x) + F_65(x) + F_78(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_74(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_4(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_31(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), 2*F_13(x) + F_65(x) + F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_60(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_13(x) + F_35(x) + F_81(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_4(x) + F_84(x))
Eq(F_84(x), F_13(x) + F_32(x) + F_85(x))
Eq(F_85(x), F_24(x)*F_4(x))
Eq(F_86(x), F_80(x) + F_87(x))
Eq(F_87(x), F_13(x) + F_78(x) + F_88(x) + F_98(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_95(x))
Eq(F_90(x), F_91(x) + F_93(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), x**2)
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_31(x)*F_4(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), 2*F_13(x) + F_88(x) + F_97(x))
Eq(F_97(x), F_4(x)*F_60(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_57(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_99(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_20(x) + F_80(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_57(x))
Eq(F_107(x), F_108(x) + F_112(x) + 2*F_13(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_90(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_108(x) + 2*F_13(x) + F_97(x))
Eq(F_112(x), F_106(x)*F_4(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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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": [[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, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[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, 1, 2], "pos": [[0, 1], [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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "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], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [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": 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