0132_0213_2130
Counting sequence:
1, 1, 2, 6, 21, 75, 258, 845, 2649, 8019, 23630, 68216, 193861, 544312, 1514024, 4180488, 11476203, 31358553, 85367436, 231691655, 627259131, 1694678721, 4570645292, 12309288446, 33108960151, 88958761210, 238792953938, 640459354110, 1716475912209, 4597182110439, 12304948384230, 32917271270801, 88012054052781, 235207063905087, 628292361963674, 1677598235875988, 4477535043557113, 11946035040663628, 31860329760370316, 84942603844967940, 226389433955578311, 603181362339742341, 1606594471156298832, 4277955120850759211, 11387868292235589231, 30306043808676496845, 80630755532439023768, 214467116815755477050, 570312397569434016619, 1516213798180879500334, 4030016742702480572630, 10709152637495081205786, 28451695291359602866701, 75573365601471869051187, 200696416338645918371274, 532872438105452237686613, 1414562430131489623844673, 3754382655368586519057003, 9962646926670441003787046, 26432173502859761796969200, 70115656308251116168674541, 185961524115420516587160736, 493127311033568043045933872, 1307448848272837318080922176, 3465946122064402280129143011, 9186541673142979142555493105, 24345408331790639068102961748, 64508719179748421042275846415, 170906126755291158721020665379, 452726756673076811336031106329, 1199100050041987791540850624580, 3175534013256352944078449893046, 8408557932324392890718512383871, 22262346971340119439981853139362, 58934048560647817989807935730074, 155994288176013593428343651717238, 412856718614666693048039996034633, 1092545085799664665825841467962303, 2890878289833177874542155334342126, 7648419817298032543167678618852185, 20233271508935361119364627557164821, 53519735710715255815874988170435031, 141552068268170553225460307819186162, 374346526003593354613768137564024716, 989891547778683183193845573850302241, 2617330174432957270559725825491026740, 6919701108587354348266402973505988628, 18292577493028738485878682180169979580, 48352842261718195373725138946147314239, 127799577622440078602048126032958619549, 337751964701998435212738458408853757080, 892540910435698881446759260342527649331, 2358418474351515437146856953785488608791, 6231273041878411293767072772248785923237, 16462528531260285505686985133128192395824, 43489137662459930000543523161387092922738, 114876231907587610798931372213038229260243, 303420775303689222833350155067229247656278, 801358398281239981799887383928425187803806, 2116290115128042505565803529930025016426770, 5588446729585360007996544826353320179784901
Generating function in Maple syntax:
-(5*x^8-51*x^7+172*x^6-288*x^5+283*x^4-170*x^3+61*x^2-12*x+1)/(2*x-1)^2/(x^2-3*x+1)^2/(x-1)^3
Generating function in latex syntax:
-\frac{5 x^{8}-51 x^{7}+172 x^{6}-288 x^{5}+283 x^{4}-170 x^{3}+61 x^{2}-12 x +1}{\left(2 x -1\right)^{2} \left(x^{2}-3 x +1\right)^{2} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-5*x**8 + 51*x**7 - 172*x**6 + 288*x**5 - 283*x**4 + 170*x**3 - 61*x**2 + 12*x - 1)/((x - 1)**3*(2*x - 1)**2*(x**2 - 3*x + 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x^2-3*x+1)^2*(x-1)^3*F(x)+5*x^8-51*x^7+172*x^6-288*x^5+283*x^4-170*x^3+61*x^2-12*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x^{2}-3 x +1\right)^{2} \left(x -1\right)^{3} F \! \left(x \right)+5 x^{8}-51 x^{7}+172 x^{6}-288 x^{5}+283 x^{4}-170 x^{3}+61 x^{2}-12 x +1 = 0
Explicit closed form in Maple syntax:
1/50*((-5*n+6)*5^(1/2)+15*n+50)*(3/2-1/2*5^(1/2))^(-n)+1/50*((5*n-6)*5^(1/2)+15*n+50)*(3/2+1/2*5^(1/2))^(-n)+1/2*n^2-2^(n-1)*n+1/2*n-2^(n+1)+1
Explicit closed form in latex syntax:
\frac{\left(\left(-5 n +6\right) \sqrt{5}+15 n +50\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{50}+\frac{\left(\left(5 n -6\right) \sqrt{5}+15 n +50\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{50}+\frac{n^{2}}{2}-2^{n -1} n +\frac{n}{2}-2^{n +1}+1
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 75
a(6) = 258
a(7) = 845
a(8) = 2649
a(n+6) = -4*a(n)+28*a(n+1)-69*a(n+2)+74*a(n+3)-39*a(n+4)+10*a(n+5)+1/2*(n+3)*(n-2), n >= 9
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) = 21
a \! \left(5\right) = 75
a \! \left(6\right) = 258
a \! \left(7\right) = 845
a \! \left(8\right) = 2649
a \! \left(n +6\right) = -4 a \! \left(n \right)+28 a \! \left(n +1\right)-69 a \! \left(n +2\right)+74 a \! \left(n +3\right)-39 a \! \left(n +4\right)+10 a \! \left(n +5\right)+\frac{\left(n +3\right) \left(n -2\right)}{2}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14691/
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[16,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[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[6,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[13,x]
F[16,x] = F[17,x]+F[30,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[19,x]
F[19,x] = F[20,x]+F[5,x]
F[20,x] = F[17,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[23,x]
F[23,x] = F[24,x]+F[27,x]
F[24,x] = F[17,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[24,x]
F[27,x] = F[21,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[31,x]+F[32,x]+F[90,x]
F[31,x] = 0
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[34,x]+F[49,x]
F[34,x] = F[35,x]+F[6,x]
F[35,x] = F[31,x]+F[36,x]+F[44,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[10,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[38,x]
F[41,x] = F[14,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[12,x]*F[41,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[13,x]+F[46,x]
F[46,x] = F[35,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[12,x]*F[46,x]
F[49,x] = F[30,x]+F[50,x]
F[50,x] = 2*F[31,x]+F[51,x]+F[71,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[53,x]+F[68,x]
F[53,x] = F[54,x]+F[66,x]
F[54,x] = F[31,x]+F[55,x]+F[64,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[57,x]+F[59,x]
F[57,x] = F[10,x]+F[58,x]
F[58,x] = F[15,x]+F[31,x]+F[36,x]
F[59,x] = F[54,x]+F[60,x]
F[60,x] = 2*F[31,x]+F[51,x]+F[61,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[21,x]+F[63,x]
F[63,x] = F[61,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[17,x]+F[54,x]
F[66,x] = F[67,x]
F[67,x] = F[12,x]*F[53,x]
F[68,x] = F[63,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[12,x]*F[68,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[62,x]+F[73,x]
F[73,x] = F[74,x]+F[88,x]
F[74,x] = 2*F[31,x]+F[75,x]+F[83,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[77,x]+F[80,x]
F[77,x] = F[25,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[12,x]*F[77,x]
F[80,x] = F[28,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[12,x]*F[80,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[27,x]+F[85,x]
F[85,x] = F[74,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[85,x]
F[88,x] = F[89,x]
F[89,x] = F[12,x]*F[73,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[65,x]+F[92,x]
F[92,x] = F[108,x]+F[93,x]
F[93,x] = F[103,x]+F[31,x]+F[94,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[34,x]+F[96,x]
F[96,x] = F[21,x]+F[97,x]
F[97,x] = 2*F[31,x]+F[75,x]+F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[27,x]
F[100,x] = F[101,x]+F[97,x]
F[101,x] = F[102,x]
F[102,x] = F[100,x]*F[12,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = F[105,x]+F[24,x]
F[105,x] = F[106,x]+F[93,x]
F[106,x] = F[107,x]
F[107,x] = F[105,x]*F[12,x]
F[108,x] = 2*F[31,x]+F[109,x]+F[118,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[111,x]+F[113,x]
F[111,x] = F[112,x]+F[14,x]
F[112,x] = F[48,x]
F[113,x] = F[114,x]+F[63,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[97,x]
F[117,x] = F[115,x]
F[118,x] = F[12,x]*F[92,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_{16}\! \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_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{30}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{5}\! \left(x \right)
F_{20}\! \left(x \right) = F_{17}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \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_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{21}\! \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_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{90}\! \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_{49}\! \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_{44}\! \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_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{10}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{35}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{30}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{51}\! \left(x \right)+F_{71}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{68}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{66}\! \left(x \right)
F_{54}\! \left(x \right) = F_{31}\! \left(x \right)+F_{55}\! \left(x \right)+F_{64}\! \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_{59}\! \left(x \right)
F_{57}\! \left(x \right) = F_{10}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)+F_{36}\! \left(x \right)
F_{59}\! \left(x \right) = F_{54}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{51}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{21}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{17}\! \left(x \right)+F_{54}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{68}\! \left(x \right) = F_{63}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{62}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{88}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{75}\! \left(x \right)+F_{83}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{25}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{28}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{27}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{74}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{65}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{108}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{103}\! \left(x \right)+F_{31}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{34}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{21}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{75}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{27}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{97}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{24}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{93}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{108}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{109}\! \left(x \right)+F_{118}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{113}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{14}\! \left(x \right)
F_{112}\! \left(x \right) = F_{48}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{63}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{97}\! \left(x \right)
F_{117}\! \left(x \right) = F_{115}\! \left(x \right)
F_{118}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \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_16(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_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_6(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_13(x))
Eq(F_16(x), F_17(x) + F_30(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_5(x))
Eq(F_20(x), F_17(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_27(x))
Eq(F_24(x), F_17(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_24(x))
Eq(F_27(x), F_21(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_90(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_49(x))
Eq(F_34(x), F_35(x) + F_6(x))
Eq(F_35(x), F_31(x) + F_36(x) + F_44(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_10(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_38(x))
Eq(F_41(x), F_14(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_12(x)*F_41(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_13(x) + F_46(x))
Eq(F_46(x), F_35(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_12(x)*F_46(x))
Eq(F_49(x), F_30(x) + F_50(x))
Eq(F_50(x), 2*F_31(x) + F_51(x) + F_71(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_68(x))
Eq(F_53(x), F_54(x) + F_66(x))
Eq(F_54(x), F_31(x) + F_55(x) + F_64(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_59(x))
Eq(F_57(x), F_10(x) + F_58(x))
Eq(F_58(x), F_15(x) + F_31(x) + F_36(x))
Eq(F_59(x), F_54(x) + F_60(x))
Eq(F_60(x), 2*F_31(x) + F_51(x) + F_61(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_21(x) + F_63(x))
Eq(F_63(x), F_61(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_17(x) + F_54(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_12(x)*F_53(x))
Eq(F_68(x), F_63(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_12(x)*F_68(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_62(x) + F_73(x))
Eq(F_73(x), F_74(x) + F_88(x))
Eq(F_74(x), 2*F_31(x) + F_75(x) + F_83(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_80(x))
Eq(F_77(x), F_25(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_12(x)*F_77(x))
Eq(F_80(x), F_28(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_12(x)*F_80(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_27(x) + F_85(x))
Eq(F_85(x), F_74(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_85(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_12(x)*F_73(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_65(x) + F_92(x))
Eq(F_92(x), F_108(x) + F_93(x))
Eq(F_93(x), F_103(x) + F_31(x) + F_94(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_34(x) + F_96(x))
Eq(F_96(x), F_21(x) + F_97(x))
Eq(F_97(x), 2*F_31(x) + F_75(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_27(x))
Eq(F_100(x), F_101(x) + F_97(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_100(x)*F_12(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x) + F_24(x))
Eq(F_105(x), F_106(x) + F_93(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_105(x)*F_12(x))
Eq(F_108(x), F_109(x) + F_118(x) + 2*F_31(x))
Eq(F_109(x), F_110(x)*F_12(x))
Eq(F_110(x), F_111(x) + F_113(x))
Eq(F_111(x), F_112(x) + F_14(x))
Eq(F_112(x), F_48(x))
Eq(F_113(x), F_114(x) + F_63(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_97(x))
Eq(F_117(x), F_115(x))
Eq(F_118(x), F_12(x)*F_92(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 1, 3], "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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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": [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", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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": [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": [[{"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], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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": [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": []}, "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": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], 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