0213_0321_1230_2130
Counting sequence:
1, 1, 2, 6, 20, 61, 173, 469, 1230, 3153, 7954, 19836, 49058, 120593, 295109, 719767, 1751124, 4252337, 10311578, 24978098, 60456504, 146238245, 353571493, 854555625, 2064842802, 4988214209, 12048578682, 29098812104, 70270923894, 169686128921, 409726812333, 989293574251, 2388596881160, 5767007708193, 13923569410194, 33615906933214, 81158621165564, 195939104670605, 473047784206653, 1142054820079037, 2757194480466038, 6656511937807473, 16070343715973826, 38797429942545684, 93665627690545002, 226129465345798945, 545925993066576565, 1317984090275028863, 3181899027119308060, 7681791071496829265, 18545497589394901482, 44772816450054425226, 108091186035536664160, 260955290686210393717, 630001955318840797045, 1520959546945890885713, 3671921684908587452058, 8864804085993912916833, 21401532007447224194282, 51667872056367984224608, 124737283395444473598334, 301142452228548646203945, 727022212464574384663005, 1755186922426283029924307, 4237396140579050392345488, 10229979356726911995500353, 24697355135705898126459554, 59624690146216170120251830, 143946736381031252162794084, 347518164660922173856616669, 838983068926489574954467405, 2025484308443051812050599077, 4889951696718001161829929886, 11805387721937226561848210833, 28500727177485185162723415538, 68806842144763908153404122284, 166114411591820216038975556530, 401035665557960596944105276209, 968185743129961192475489126693, 2337407152594466235725580484711, 5643000049747252957018200109924, 13623407254716134479232330691313, 32889814564011626791875258448314, 79403036391627014561937144544354, 191695887363612549620566591436040, 462794811148918738883234065227717, 1117285509716751172670969800558277, 2697365830684135748294089526721465, 6512017171272105103692163530856578, 15721400173572444199464282204334081, 37954817519049888844908524092656858, 91631035212836297909788006835534840, 221216887946863554271064875978645254, 534064811110501447421292569606763321, 1289346510175109635710111840666915725, 3112757831474043016013933225444195387, 7514862173147699192476231902347589016, 18142482177814510409473529440910000481, 43799826528859614841841093780234100274, 105742135235686207456818906019007621006, 255284097000512460958067030242715899724
Generating function in Maple syntax:
(x^7-2*x^6-3*x^5+2*x^4+2*x^3+4*x^2-4*x+1)/(x^2+2*x-1)/(x^3+x^2+x-1)/(x-1)^2
Generating function in latex syntax:
\frac{x^{7}-2 x^{6}-3 x^{5}+2 x^{4}+2 x^{3}+4 x^{2}-4 x +1}{\left(x^{2}+2 x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(x**7 - 2*x**6 - 3*x**5 + 2*x**4 + 2*x**3 + 4*x**2 - 4*x + 1)/((x - 1)**2*(x**2 + 2*x - 1)*(x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2+2*x-1)*(x^3+x^2+x-1)*(x-1)^2*F(x)-x^7+2*x^6+3*x^5-2*x^4-2*x^3-4*x^2+4*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}+2 x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2} F \! \left(x \right)-x^{7}+2 x^{6}+3 x^{5}-2 x^{4}-2 x^{3}-4 x^{2}+4 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/1056*(((64*11^(1/2)-220*I)*3^(1/2)+192*I*11^(1/2)-220)*(17+3*11^(1/2)*3^(1/2))^(1/3)-968+((-107*11^(1/2)-649*I)*3^(1/2)+321*I*11^(1/2)+649)*(17+3*11^(1/2)*3^(1/2))^(2/3))*(1/24*((17*I+3*11^(1/2))*3^(1/2)-9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/1056*(((-107*11^(1/2)+649*I)*3^(1/2)-321*I*11^(1/2)+649)*(17+3*11^(1/2)*3^(1/2))^(2/3)-968+((64*11^(1/2)+220*I)*3^(1/2)-192*I*11^(1/2)-220)*(17+3*11^(1/2)*3^(1/2))^(1/3))*(1/24*((-17*I+3*11^(1/2))*3^(1/2)+9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/1056*((214*11^(1/2)*3^(1/2)-1298)*(17+3*11^(1/2)*3^(1/2))^(2/3)-128*(17+3*11^(1/2)*3^(1/2))^(1/3)*11^(1/2)*3^(1/2)+440*(17+3*11^(1/2)*3^(1/2))^(1/3)-968)*(1/3*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3+17/12*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/4*(17+3*11^(1/2)*3^(1/2))^(2/3)*11^(1/2)*3^(1/2))^(-n)+1/1056*(-726*2^(1/2)+396)*(-1-2^(1/2))^(-n)+1/1056*(726*2^(1/2)+396)*(2^(1/2)-1)^(-n)+1/4*n+2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(\left(64 \sqrt{11}-220 \,\mathrm{I}\right) \sqrt{3}+192 \,\mathrm{I} \sqrt{11}-220\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}-968+\left(\left(-107 \sqrt{11}-649 \,\mathrm{I}\right) \sqrt{3}+321 \,\mathrm{I} \sqrt{11}+649\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}-\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{1056}\\+\\\frac{\left(\left(\left(-107 \sqrt{11}+649 \,\mathrm{I}\right) \sqrt{3}-321 \,\mathrm{I} \sqrt{11}+649\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}-968+\left(\left(64 \sqrt{11}+220 \,\mathrm{I}\right) \sqrt{3}-192 \,\mathrm{I} \sqrt{11}-220\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}+\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{1056}\\+\\\frac{\left(\left(214 \sqrt{11}\, \sqrt{3}-1298\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}-128 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{11}\, \sqrt{3}+440 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}-968\right) \left(\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}-\frac{1}{3}+\frac{17 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{12}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{11}\, \sqrt{3}}{4}\right)^{-n}}{1056}\\+\frac{\left(-726 \sqrt{2}+396\right) \left(-1-\sqrt{2}\right)^{-n}}{1056}+\frac{\left(726 \sqrt{2}+396\right) \left(\sqrt{2}-1\right)^{-n}}{1056}+\frac{n}{4}\\+2 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 61
a(6) = 173
a(7) = 469
a(n+2) = -1/2*a(n)-3/2*a(n+1)+3/2*a(n+4)-1/2*a(n+5)+1/2*n+4, 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) = 20
a \! \left(5\right) = 61
a \! \left(6\right) = 173
a \! \left(7\right) = 469
a \! \left(n +2\right) = -\frac{a \! \left(n \right)}{2}-\frac{3 a \! \left(n +1\right)}{2}+\frac{3 a \! \left(n +4\right)}{2}-\frac{a \! \left(n +5\right)}{2}+\frac{n}{2}+4, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15738/
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[12,x]*F[4,x]
F[4,x] = F[17,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[13,x]
F[12,x] = x
F[13,x] = F[1,x]+F[12,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[9,x]
F[17,x] = F[18,x]+F[30,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[1,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[13,x]
F[24,x] = F[18,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[18,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[18,x]
F[30,x] = F[31,x]+F[32,x]+F[66,x]
F[31,x] = 0
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[34,x]+F[50,x]
F[34,x] = F[35,x]+F[6,x]
F[35,x] = F[31,x]+F[36,x]+F[42,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[6,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]+F[38,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[41,x]+F[44,x]
F[44,x] = F[45,x]+F[47,x]
F[45,x] = F[46,x]
F[46,x] = x^2
F[47,x] = F[48,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[44,x]
F[50,x] = F[30,x]+F[51,x]
F[51,x] = 2*F[31,x]+F[52,x]+F[58,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[30,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[28,x]+F[54,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[57,x]+F[60,x]
F[60,x] = F[61,x]+F[63,x]
F[61,x] = F[62,x]
F[62,x] = F[12,x]*F[28,x]
F[63,x] = F[64,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[60,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[17,x]+F[68,x]
F[68,x] = F[69,x]+F[79,x]
F[69,x] = F[31,x]+F[70,x]+F[78,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[12,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = x^2
F[75,x] = F[28,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[12,x]*F[28,x]
F[78,x] = F[12,x]*F[27,x]
F[79,x] = 2*F[31,x]+F[80,x]+F[84,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[38,x]
F[83,x] = F[54,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[68,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{17}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{24}\! \left(x \right) = F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{66}\! \left(x \right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{50}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)+F_{36}\! \left(x \right)+F_{42}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{6}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right)+F_{38}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = x^{2}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = F_{30}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{52}\! \left(x \right)+F_{58}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{30}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{28}\! \left(x \right)+F_{54}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{57}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{60}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{17}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{79}\! \left(x \right)
F_{69}\! \left(x \right) = F_{31}\! \left(x \right)+F_{70}\! \left(x \right)+F_{78}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = x^{2}
F_{75}\! \left(x \right) = F_{28}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{80}\! \left(x \right)+F_{84}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{38}\! \left(x \right)
F_{83}\! \left(x \right) = F_{54}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{68}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_17(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_13(x))
Eq(F_12(x), x)
Eq(F_13(x), F_1(x) + F_12(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_9(x))
Eq(F_17(x), F_18(x) + F_30(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_1(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_13(x))
Eq(F_24(x), F_18(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_18(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_18(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_66(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_50(x))
Eq(F_34(x), F_35(x) + F_6(x))
Eq(F_35(x), F_31(x) + F_36(x) + F_42(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_6(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x) + F_38(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_41(x) + F_44(x))
Eq(F_44(x), F_45(x) + F_47(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), x**2)
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_44(x))
Eq(F_50(x), F_30(x) + F_51(x))
Eq(F_51(x), 2*F_31(x) + F_52(x) + F_58(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_30(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_28(x) + F_54(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_57(x) + F_60(x))
Eq(F_60(x), F_61(x) + F_63(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_12(x)*F_28(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_60(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_17(x) + F_68(x))
Eq(F_68(x), F_69(x) + F_79(x))
Eq(F_69(x), F_31(x) + F_70(x) + F_78(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_12(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), x**2)
Eq(F_75(x), F_28(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_12(x)*F_28(x))
Eq(F_78(x), F_12(x)*F_27(x))
Eq(F_79(x), 2*F_31(x) + F_80(x) + F_84(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_38(x))
Eq(F_83(x), F_54(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_68(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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"comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 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", 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[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[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, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], 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