0213_0231_0312_1230_3012

Counting sequence:
1, 1, 2, 6, 19, 58, 174, 528, 1649, 5328, 17764, 60767, 212029, 751000, 2690718, 9727492, 35423069, 129775708, 477900672, 1767787287, 6565168785, 24468363940, 91486757690, 343068001981, 1289920924239, 4861979955558, 18367420180664, 69533685133353, 263748220185409, 1002242753521844, 3814987575833662, 14544638186710060, 55534069172014965, 212336139002177140, 812944059329599352, 3116285529267038999, 11959798454579929561, 45950804462060695132, 176733863061884607602, 680425372279731613497, 2622127043376003735775, 10113918593836921388710, 39044429916302490469440, 150853479213881444681961, 583300119610588879131465, 2257117854112432445341516, 8740328711603542134222902, 33868773757331784374783689, 131327898242450840454701379, 509552245180180088008028658, 1978261657757286553530615804, 7684785670516568185044500077, 29869166945777129549769786629, 116157871455791441449808585440, 451959718027971485846118989922, 1759414616608854899789498838399, 6852456927844945555143696390651, 26700952856774996019433296766882, 104088460289122592263874470522112, 405944995127577562191395746788829, 1583850964596121195608277385884041, 6182127958584857956330090060908396, 24139737743045631437397476973659262, 94295850558771989011307421801153916, 368479169875816677925753116423096485, 1440418573150919705765978041662966436, 5632681584560312808780892000687349352, 22033725021956517610932505203733360599, 86218923998960286021333545843053932009, 337485502510215976147079603813764273996, 1321422108420282271670533797907640845538, 5175569924646105561780123435429888320641, 20276890389709399867651365051124286236767, 79463489365077377850652970598088559309190, 311496878311103321156425757450287714879248, 1221395654430378811866539653870919292497737, 4790408930363303911403944072120778784440729, 18793142726809884575362477006539373840085308, 73745243611532458459992383309550986533009062, 289450081175264899454888308939298081851742157, 1136359577947336271932841802824282085842316875, 4462290049988320482465659149145362441849063770, 17526585015616776834739976221194114153095055580, 68854441132780194707897723441225564176382852021, 270557451039395118028661806102282400487466575685, 1063353702922273835973075343669704126856693998496, 4180080073556524734514773199423362794695932505842, 16435314834665426797069299703267796815901952781639, 64633260585762914370496946971156002807750260038139, 254224158304000796523954059748861289776684821584706, 1000134600800354781929400488476581149742735989070928, 3935312233584004685417856048643428080534581478268061, 15487357822491889407128331915538500373535030724328217, 60960876535340415751462573484349963175011928100427420, 239993345518077005168915796430517351572365225874212718, 944973797977428207852605910069020853969399555006874657, 3721443204405954385563870620607409173973844290922639979, 14657929356129575437016878005113357790241630137987651018, 57743358069601357782187700924955506391078081998932407492, 227508830794229349661819541029514154070156383349892645077, 896519947090131496687170071341751232649066923035449109645

Generating function in Maple syntax:
1/2*(-2*(x-1/2)*(-1+x)^3*(1-4*x)^(1/2)+4*x^4-7*x^3+9*x^2-5*x+1)/x/(2*x-1)/(-1+x)^3

Generating function in latex syntax:
\frac{-2 \left(x -\frac{1}{2}\right) \left(-1+x \right)^{3} \sqrt{1-4 x}+4 x^{4}-7 x^{3}+9 x^{2}-5 x +1}{2 x \left(2 x -1\right) \left(-1+x \right)^{3}}

Generating function in sympy syntax:
(2*x**4 - 7*x**3/2 + 9*x**2/2 - 5*x/2 + sqrt(1 - 4*x)*(1 - 2*x)*(x - 1)**3/2 + 1/2)/(x*(x - 1)**3*(2*x - 1))

Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(-1+x)^6*F(x)^2-(2*x-1)*(4*x^4-7*x^3+9*x^2-5*x+1)*(-1+x)^3*F(x)+(4*x^4-9*x^3+10*x^2-5*x+1)*(x^4-4*x^3+8*x^2-5*x+1) = 0

Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(-1+x \right)^{6} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(4 x^{4}-7 x^{3}+9 x^{2}-5 x +1\right) \left(-1+x \right)^{3} F \! \left(x \right)+\left(4 x^{4}-9 x^{3}+10 x^{2}-5 x +1\right) \left(x^{4}-4 x^{3}+8 x^{2}-5 x +1\right) = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 58
a(6) = 174
a(n+3) = 8*(2*n+1)/(n+4)*a(n)-4*(5*n+8)/(n+4)*a(n+1)+2*(4*n+11)/(n+4)*a(n+2)+1/2*(3*n^3-17*n^2-4*n+8)/(n+4), n >= 7

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) = 58
a \! \left(6\right) = 174
a \! \left(n +3\right) = \frac{8 \left(2 n +1\right) a \! \left(n \right)}{n +4}-\frac{4 \left(5 n +8\right) a \! \left(n +1\right)}{n +4}+\frac{2 \left(4 n +11\right) a \! \left(n +2\right)}{n +4}+\frac{3 n^{3}-17 n^{2}-4 n +8}{2 n +8}, \quad n \geq 7

Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://www.permpal.com/tree/21806/
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[9,x]
F[4,x] = F[109,x]+F[5,x]
F[5,x] = F[10,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[6,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[53,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[9,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[9,x]
F[17,x] = F[18,x]+F[30,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[9,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[1,x]+F[9,x]
F[22,x] = F[18,x]+F[23,x]
F[23,x] = F[24,x]+F[25,x]+F[29,x]
F[24,x] = 0
F[25,x] = F[26,x]*F[9,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[9,x]
F[28,x] = F[23,x]
F[29,x] = F[18,x]*F[9,x]
F[30,x] = F[24,x]+F[31,x]+F[51,x]
F[31,x] = F[32,x]*F[9,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[15,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[15,x]*F[9,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = 2*F[24,x]+F[38,x]+F[42,x]
F[38,x] = F[39,x]*F[9,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[34,x]
F[41,x] = F[37,x]
F[42,x] = F[43,x]*F[9,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]*F[9,x]
F[45,x] = F[33,x]+F[46,x]
F[46,x] = F[43,x]+F[47,x]
F[47,x] = 2*F[24,x]+F[42,x]+F[48,x]
F[48,x] = F[49,x]*F[9,x]
F[49,x] = F[40,x]+F[50,x]
F[50,x] = F[47,x]
F[51,x] = F[52,x]*F[9,x]
F[52,x] = F[18,x]+F[43,x]
F[53,x] = F[24,x]+F[54,x]+F[81,x]
F[54,x] = F[55,x]*F[9,x]
F[55,x] = F[56,x]+F[59,x]
F[56,x] = F[57,x]+F[7,x]
F[57,x] = F[58,x]
F[58,x] = F[56,x]*F[9,x]
F[59,x] = F[60,x]+F[86,x]
F[60,x] = F[24,x]+F[61,x]+F[81,x]
F[61,x] = F[62,x]*F[9,x]
F[62,x] = F[63,x]+F[66,x]
F[63,x] = F[64,x]+F[7,x]
F[64,x] = F[65,x]
F[65,x] = F[7,x]*F[9,x]
F[66,x] = F[60,x]+F[67,x]
F[67,x] = 2*F[24,x]+F[68,x]+F[72,x]
F[68,x] = F[69,x]*F[9,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[64,x]
F[71,x] = F[67,x]
F[72,x] = F[73,x]*F[9,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]*F[9,x]
F[75,x] = F[63,x]+F[76,x]
F[76,x] = F[73,x]+F[77,x]
F[77,x] = 2*F[24,x]+F[72,x]+F[78,x]
F[78,x] = F[79,x]*F[9,x]
F[79,x] = F[70,x]+F[80,x]
F[80,x] = F[77,x]
F[81,x] = F[82,x]*F[9,x]
F[82,x] = F[7,x]+F[83,x]
F[83,x] = F[24,x]+F[81,x]+F[84,x]
F[84,x] = F[85,x]*F[9,x]
F[85,x] = F[7,x]+F[83,x]
F[86,x] = 2*F[24,x]+F[107,x]+F[87,x]
F[87,x] = F[88,x]*F[9,x]
F[88,x] = F[89,x]+F[92,x]
F[89,x] = F[57,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[57,x]*F[9,x]
F[92,x] = F[86,x]+F[93,x]
F[93,x] = 3*F[24,x]+F[94,x]+F[98,x]
F[94,x] = F[9,x]*F[95,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[90,x]
F[97,x] = F[93,x]
F[98,x] = F[9,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[9,x]
F[101,x] = F[102,x]+F[89,x]
F[102,x] = F[103,x]+F[99,x]
F[103,x] = 3*F[24,x]+F[104,x]+F[98,x]
F[104,x] = F[105,x]*F[9,x]
F[105,x] = F[106,x]+F[96,x]
F[106,x] = F[103,x]
F[107,x] = F[108,x]*F[9,x]
F[108,x] = F[73,x]+F[99,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x,1]
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]*F[123,x,k[0]]*F[9,x]
F[114,x,k[0]] = F[115,x,k[0]]+F[133,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]+F[82,x]
F[116,x,k[0]] = F[117,x,k[0]]+F[124,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[9,x]
F[119,x,k[0]] = F[117,x,k[0]]+F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]*F[123,x,k[0]]
F[122,x,k[0]] = k[0]*x
F[123,x,k[0]] = F[1,x]+F[120,x,k[0]]
F[124,x,k[0]] = 2*F[24,x]+F[125,x,k[0]]+F[132,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]*F[9,x]
F[126,x,k[0]] = F[124,x,k[0]]+F[127,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]+F[130,x,k[0]]+F[24,x]
F[128,x,k[0]] = F[122,x,k[0]]*F[129,x,k[0]]
F[129,x,k[0]] = F[127,x,k[0]]+F[7,x]
F[130,x,k[0]] = F[131,x,k[0]]*F[9,x]
F[131,x,k[0]] = F[120,x,k[0]]+F[127,x,k[0]]
F[132,x,k[0]] = F[116,x,k[0]]*F[9,x]
F[133,x,k[0]] = (F[112,x,k[0]]*k[0]-F[112,x,1])/(-1+k[0])
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_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{109}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \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_{6}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{53}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{9}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \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_{20}\! \left(x \right) F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{9}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{9}\! \left(x \right)
F_{28}\! \left(x \right) = F_{23}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)+F_{51}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{9}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{15}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{38}\! \left(x \right)+F_{42}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{9}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right) F_{9}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right) F_{9}\! \left(x \right)
F_{45}\! \left(x \right) = F_{33}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{42}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right) F_{9}\! \left(x \right)
F_{49}\! \left(x \right) = F_{40}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{9}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right)+F_{43}\! \left(x \right)
F_{53}\! \left(x \right) = F_{24}\! \left(x \right)+F_{54}\! \left(x \right)+F_{81}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{9}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{59}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{7}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{56}\! \left(x \right) F_{9}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{86}\! \left(x \right)
F_{60}\! \left(x \right) = F_{24}\! \left(x \right)+F_{61}\! \left(x \right)+F_{81}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right) F_{9}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{66}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{7}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{66}\! \left(x \right) = F_{60}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{68}\! \left(x \right)+F_{72}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right) F_{9}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{64}\! \left(x \right)
F_{71}\! \left(x \right) = F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right) F_{9}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right) F_{9}\! \left(x \right)
F_{75}\! \left(x \right) = F_{63}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right) F_{9}\! \left(x \right)
F_{79}\! \left(x \right) = F_{70}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{77}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right) F_{9}\! \left(x \right)
F_{82}\! \left(x \right) = F_{7}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{24}\! \left(x \right)+F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right) F_{9}\! \left(x \right)
F_{85}\! \left(x \right) = F_{7}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{107}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right) F_{9}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{92}\! \left(x \right)
F_{89}\! \left(x \right) = F_{57}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{57}\! \left(x \right) F_{9}\! \left(x \right)
F_{92}\! \left(x \right) = F_{86}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 3 F_{24}\! \left(x \right)+F_{94}\! \left(x \right)+F_{98}\! \left(x \right)
F_{94}\! \left(x \right) = F_{9}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{90}\! \left(x \right)
F_{97}\! \left(x \right) = F_{93}\! \left(x \right)
F_{98}\! \left(x \right) = F_{9}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{9}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{89}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{99}\! \left(x \right)
F_{103}\! \left(x \right) = 3 F_{24}\! \left(x \right)+F_{104}\! \left(x \right)+F_{98}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{9}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{96}\! \left(x \right)
F_{106}\! \left(x \right) = F_{103}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{9}\! \left(x \right)
F_{108}\! \left(x \right) = F_{73}\! \left(x \right)+F_{99}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x , 1\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{123}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{82}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{123}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = y x
F_{123}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{120}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = 2 F_{24}\! \left(x \right)+F_{125}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{130}\! \left(x , y\right)+F_{24}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{133}\! \left(x , y\right) = \frac{F_{112}\! \left(x , y\right) y -F_{112}\! \left(x , 1\right)}{-1+y}
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_9(x))
Eq(F_4(x), F_109(x) + F_5(x))
Eq(F_5(x), F_10(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_6(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_53(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_9(x))
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(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_20(x)*F_9(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_1(x) + F_9(x))
Eq(F_22(x), F_18(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_29(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_26(x)*F_9(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_9(x))
Eq(F_28(x), F_23(x))
Eq(F_29(x), F_18(x)*F_9(x))
Eq(F_30(x), F_24(x) + F_31(x) + F_51(x))
Eq(F_31(x), F_32(x)*F_9(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_15(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_15(x)*F_9(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), 2*F_24(x) + F_38(x) + F_42(x))
Eq(F_38(x), F_39(x)*F_9(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_34(x))
Eq(F_41(x), F_37(x))
Eq(F_42(x), F_43(x)*F_9(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x)*F_9(x))
Eq(F_45(x), F_33(x) + F_46(x))
Eq(F_46(x), F_43(x) + F_47(x))
Eq(F_47(x), 2*F_24(x) + F_42(x) + F_48(x))
Eq(F_48(x), F_49(x)*F_9(x))
Eq(F_49(x), F_40(x) + F_50(x))
Eq(F_50(x), F_47(x))
Eq(F_51(x), F_52(x)*F_9(x))
Eq(F_52(x), F_18(x) + F_43(x))
Eq(F_53(x), F_24(x) + F_54(x) + F_81(x))
Eq(F_54(x), F_55(x)*F_9(x))
Eq(F_55(x), F_56(x) + F_59(x))
Eq(F_56(x), F_57(x) + F_7(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_56(x)*F_9(x))
Eq(F_59(x), F_60(x) + F_86(x))
Eq(F_60(x), F_24(x) + F_61(x) + F_81(x))
Eq(F_61(x), F_62(x)*F_9(x))
Eq(F_62(x), F_63(x) + F_66(x))
Eq(F_63(x), F_64(x) + F_7(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_7(x)*F_9(x))
Eq(F_66(x), F_60(x) + F_67(x))
Eq(F_67(x), 2*F_24(x) + F_68(x) + F_72(x))
Eq(F_68(x), F_69(x)*F_9(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_64(x))
Eq(F_71(x), F_67(x))
Eq(F_72(x), F_73(x)*F_9(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x)*F_9(x))
Eq(F_75(x), F_63(x) + F_76(x))
Eq(F_76(x), F_73(x) + F_77(x))
Eq(F_77(x), 2*F_24(x) + F_72(x) + F_78(x))
Eq(F_78(x), F_79(x)*F_9(x))
Eq(F_79(x), F_70(x) + F_80(x))
Eq(F_80(x), F_77(x))
Eq(F_81(x), F_82(x)*F_9(x))
Eq(F_82(x), F_7(x) + F_83(x))
Eq(F_83(x), F_24(x) + F_81(x) + F_84(x))
Eq(F_84(x), F_85(x)*F_9(x))
Eq(F_85(x), F_7(x) + F_83(x))
Eq(F_86(x), F_107(x) + 2*F_24(x) + F_87(x))
Eq(F_87(x), F_88(x)*F_9(x))
Eq(F_88(x), F_89(x) + F_92(x))
Eq(F_89(x), F_57(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_57(x)*F_9(x))
Eq(F_92(x), F_86(x) + F_93(x))
Eq(F_93(x), 3*F_24(x) + F_94(x) + F_98(x))
Eq(F_94(x), F_9(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_90(x))
Eq(F_97(x), F_93(x))
Eq(F_98(x), F_9(x)*F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_9(x))
Eq(F_101(x), F_102(x) + F_89(x))
Eq(F_102(x), F_103(x) + F_99(x))
Eq(F_103(x), F_104(x) + 3*F_24(x) + F_98(x))
Eq(F_104(x), F_105(x)*F_9(x))
Eq(F_105(x), F_106(x) + F_96(x))
Eq(F_106(x), F_103(x))
Eq(F_107(x), F_108(x)*F_9(x))
Eq(F_108(x), F_73(x) + F_99(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x, 1))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0)*F_123(x, k_0)*F_9(x))
Eq(F_114(x, k_0), F_115(x, k_0) + F_133(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0) + F_82(x))
Eq(F_116(x, k_0), F_117(x, k_0) + F_124(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_9(x))
Eq(F_119(x, k_0), F_117(x, k_0) + F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0)*F_123(x, k_0))
Eq(F_122(x, k_0), k_0*x)
Eq(F_123(x, k_0), F_1(x) + F_120(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0) + F_132(x, k_0) + 2*F_24(x))
Eq(F_125(x, k_0), F_126(x, k_0)*F_9(x))
Eq(F_126(x, k_0), F_124(x, k_0) + F_127(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0) + F_130(x, k_0) + F_24(x))
Eq(F_128(x, k_0), F_122(x, k_0)*F_129(x, k_0))
Eq(F_129(x, k_0), F_127(x, k_0) + F_7(x))
Eq(F_130(x, k_0), F_131(x, k_0)*F_9(x))
Eq(F_131(x, k_0), F_120(x, k_0) + F_127(x, k_0))
Eq(F_132(x, k_0), F_116(x, k_0)*F_9(x))
Eq(F_133(x, k_0), (-k_0*F_112(x, k_0) + F_112(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 2, "strategy_class": "RequirementInsertionFactory"}, {"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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "requirement_placements_tracked_fusion", "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 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, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [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]]}, 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