0132_0213_0321_1230
Counting sequence:
1, 1, 2, 6, 20, 65, 204, 624, 1874, 5550, 16252, 47139, 135608, 387328, 1099364, 3103098, 8715980, 24374741, 67900068, 188487408, 521588918, 1439263206, 3961256572, 10876952391, 29802406640, 81497288320, 222459811784, 606230380914, 1649514067724, 4481828575865, 12161272738332, 32958443229744, 89218250861978, 241252705934238, 651705399634684, 1758804768215403, 4742369345537960, 12776347609699456, 34393154656871468, 92514532719416298, 248678245763308748, 667992263717279261, 1793187058005859092, 4810762663883425776, 12898794231532285310, 34565507270305531350, 92577698199296000764, 247827616345771956879, 663105276068769657824, 1773428576126782938880, 4740801455063939226512, 12667898503424613199074, 33836041336273764033548, 90340744915703668142273, 241114604923644297873804, 643287786109243315522608, 1715674492905120675029090, 4574228199358809325896846, 12191561894935543380063868, 32483620366002236939651763, 86524236090998976756523928, 230400735762281299195388416, 613347978017892117184269812, 1632341571190480411707549786, 4343101848005218751937560780, 11552540938434020891359394405, 30721826753977552439117920644, 81679279722543602948099388144, 217107727833330819491372783174, 576952709655883322336201110470, 1532885103386838473009003559292, 4071797901457542582650784657879, 10813659801739575359921179087568, 28712539805364779171265616359808, 76222883319002058901715138235224, 202309522965160283723962750624338, 536867000314749337334017324836620, 1424422009385102843762408550417161, 3778629307329778728308061385238268, 10022026219684766294673494036090928, 26576899993514678413755680118300458, 70466465379224768630937520397234046, 186806420357617084001497372560244732, 495146776715935584711435754959282171, 1312231928644263980533820188445457800, 3477149084757979112574789170259583360, 9212417533401385165483059364202324924, 24404110063225024756345619204770821834, 64638730091848193819231894088909048524, 171184525971283565289026954362724915885, 453293367663358708721429215196363165172, 1200158690783974543560779874784069580784, 3177193526142909405848798386166225505038, 8409991238242914627973581376256766497718, 22258477418926591826167598733357622312444, 58903963358962209880867493083809484973343, 155863282448897803439432633067847236132800, 412376971020124100036242527030167645963776, 1090931021917725333363047841246384758843168, 2885715181619431317575976121554136765268418, 7632448392293495649321610136896543655960588
Generating function in Maple syntax:
(x^7-7*x^6+23*x^5-50*x^4+56*x^3-32*x^2+9*x-1)/(-1+2*x)/(x-1)^2/(x^2-3*x+1)^2
Generating function in latex syntax:
\frac{x^{7}-7 x^{6}+23 x^{5}-50 x^{4}+56 x^{3}-32 x^{2}+9 x -1}{\left(-1+2 x \right) \left(x -1\right)^{2} \left(x^{2}-3 x +1\right)^{2}}
Generating function in sympy syntax:
(x**7 - 7*x**6 + 23*x**5 - 50*x**4 + 56*x**3 - 32*x**2 + 9*x - 1)/((x - 1)**2*(2*x - 1)*(x**2 - 3*x + 1)**2)
Implicit equation for the generating function in Maple syntax:
(-1+2*x)*(x-1)^2*(x^2-3*x+1)^2*F(x)-x^7+7*x^6-23*x^5+50*x^4-56*x^3+32*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(-1+2 x \right) \left(x -1\right)^{2} \left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)-x^{7}+7 x^{6}-23 x^{5}+50 x^{4}-56 x^{3}+32 x^{2}-9 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/50*((5*n+18)*5^(1/2)-5*n-50)*(3/2-1/2*5^(1/2))^(-n)+1/50*((-5*n-18)*5^(1/2)-5*n-50)*(3/2+1/2*5^(1/2))^(-n)-n+2^(n-1)+2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(5 n +18\right) \sqrt{5}-5 n -50\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{50}+\\\frac{\left(\left(-5 n -18\right) \sqrt{5}-5 n -50\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{50}-n +2^{n -1}+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) = 65
a(6) = 204
a(7) = 624
a(n+5) = 2*a(n)-13*a(n+1)+28*a(n+2)-23*a(n+3)+8*a(n+4)+n-1, 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) = 65
a \! \left(6\right) = 204
a \! \left(7\right) = 624
a \! \left(n +5\right) = 2 a \! \left(n \right)-13 a \! \left(n +1\right)+28 a \! \left(n +2\right)-23 a \! \left(n +3\right)+8 a \! \left(n +4\right)+n -1, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15253/
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[19,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[12,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[59,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,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[12,x]*F[16,x]
F[26,x] = F[20,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]+F[57,x]
F[28,x] = 0
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[31,x]+F[35,x]
F[31,x] = F[24,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[12,x]
F[35,x] = F[27,x]+F[36,x]
F[36,x] = 2*F[28,x]+F[37,x]+F[41,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[32,x]
F[40,x] = F[36,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[28,x]+F[44,x]+F[56,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[12,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = x^2
F[49,x] = F[43,x]+F[50,x]
F[50,x] = 2*F[28,x]+F[51,x]+F[55,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[47,x]
F[54,x] = F[50,x]
F[55,x] = F[12,x]*F[43,x]
F[56,x] = F[12,x]*F[20,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[20,x]+F[43,x]
F[59,x] = F[129,x]+F[28,x]+F[60,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[62,x]+F[76,x]
F[62,x] = F[6,x]+F[63,x]
F[63,x] = F[28,x]+F[64,x]+F[69,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[10,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[12,x]+F[66,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[68,x]+F[71,x]
F[71,x] = F[72,x]+F[74,x]
F[72,x] = F[73,x]
F[73,x] = x^2
F[74,x] = F[75,x]
F[75,x] = F[12,x]*F[71,x]
F[76,x] = F[59,x]+F[77,x]
F[77,x] = F[100,x]+F[122,x]+F[28,x]+F[78,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[80,x]+F[84,x]
F[80,x] = F[63,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[66,x]
F[84,x] = F[77,x]+F[85,x]
F[85,x] = 2*F[28,x]+F[86,x]+F[90,x]+F[99,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[81,x]
F[89,x] = F[85,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = 2*F[28,x]+F[93,x]+F[97,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[66,x]
F[96,x] = F[92,x]
F[97,x] = F[12,x]*F[98,x]
F[98,x] = F[43,x]+F[92,x]
F[99,x] = 0
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[102,x]+F[92,x]
F[102,x] = F[103,x]+F[120,x]+F[28,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = F[105,x]+F[107,x]
F[105,x] = F[10,x]+F[106,x]
F[106,x] = F[28,x]+F[64,x]+F[67,x]
F[107,x] = F[102,x]+F[108,x]
F[108,x] = F[100,x]+F[109,x]+F[28,x]+F[97,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[111,x]+F[113,x]
F[111,x] = F[106,x]+F[112,x]
F[112,x] = F[82,x]
F[113,x] = F[108,x]+F[114,x]
F[114,x] = 2*F[28,x]+F[115,x]+F[119,x]+F[90,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[112,x]
F[118,x] = F[114,x]
F[119,x] = 0
F[120,x] = F[12,x]*F[121,x]
F[121,x] = F[102,x]+F[20,x]
F[122,x] = F[12,x]*F[123,x]
F[123,x] = F[124,x]+F[98,x]
F[124,x] = F[125,x]+F[127,x]
F[125,x] = F[126,x]
F[126,x] = F[12,x]*F[43,x]
F[127,x] = F[128,x]
F[128,x] = F[12,x]*F[124,x]
F[129,x] = F[12,x]*F[130,x]
F[130,x] = F[121,x]+F[131,x]
F[131,x] = F[132,x]+F[134,x]
F[132,x] = F[133,x]+F[28,x]+F[44,x]
F[133,x] = F[12,x]*F[58,x]
F[134,x] = 2*F[28,x]+F[135,x]+F[93,x]
F[135,x] = F[12,x]*F[131,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_{19}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{59}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \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_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{57}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right)
F_{35}\! \left(x \right) = F_{27}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{28}\! \left(x \right)+F_{44}\! \left(x \right)+F_{56}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = x^{2}
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \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_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{47}\! \left(x \right)
F_{54}\! \left(x \right) = F_{50}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{20}\! \left(x \right)+F_{43}\! \left(x \right)
F_{59}\! \left(x \right) = F_{129}\! \left(x \right)+F_{28}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{76}\! \left(x \right)
F_{62}\! \left(x \right) = F_{6}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{28}\! \left(x \right)+F_{64}\! \left(x \right)+F_{69}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{10}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = x^{2}
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{76}\! \left(x \right) = F_{59}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{100}\! \left(x \right)+F_{122}\! \left(x \right)+F_{28}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{84}\! \left(x \right)
F_{80}\! \left(x \right) = F_{63}\! \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_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{66}\! \left(x \right)
F_{84}\! \left(x \right) = F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{86}\! \left(x \right)+F_{90}\! \left(x \right)+F_{99}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{81}\! \left(x \right)
F_{89}\! \left(x \right) = F_{85}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{93}\! \left(x \right)+F_{97}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{66}\! \left(x \right)
F_{96}\! \left(x \right) = F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{43}\! \left(x \right)+F_{92}\! \left(x \right)
F_{99}\! \left(x \right) = 0
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{92}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{120}\! \left(x \right)+F_{28}\! \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_{107}\! \left(x \right)
F_{105}\! \left(x \right) = F_{10}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{28}\! \left(x \right)+F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{107}\! \left(x \right) = F_{102}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{100}\! \left(x \right)+F_{109}\! \left(x \right)+F_{28}\! \left(x \right)+F_{97}\! \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_{106}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{82}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{115}\! \left(x \right)+F_{119}\! \left(x \right)+F_{90}\! \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_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{112}\! \left(x \right)
F_{118}\! \left(x \right) = F_{114}\! \left(x \right)
F_{119}\! \left(x \right) = 0
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{102}\! \left(x \right)+F_{20}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{98}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{127}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right) F_{124}\! \left(x \right)
F_{129}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{121}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{134}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{28}\! \left(x \right)+F_{44}\! \left(x \right)
F_{133}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{134}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{135}\! \left(x \right)+F_{93}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{131}\! \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_19(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_12(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_13(x))
Eq(F_19(x), F_20(x) + F_59(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(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_12(x)*F_16(x))
Eq(F_26(x), F_20(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_57(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_35(x))
Eq(F_31(x), F_24(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_12(x))
Eq(F_35(x), F_27(x) + F_36(x))
Eq(F_36(x), 2*F_28(x) + F_37(x) + F_41(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_32(x))
Eq(F_40(x), F_36(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_28(x) + F_44(x) + F_56(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_12(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), x**2)
Eq(F_49(x), F_43(x) + F_50(x))
Eq(F_50(x), 2*F_28(x) + F_51(x) + F_55(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_47(x))
Eq(F_54(x), F_50(x))
Eq(F_55(x), F_12(x)*F_43(x))
Eq(F_56(x), F_12(x)*F_20(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_20(x) + F_43(x))
Eq(F_59(x), F_129(x) + F_28(x) + F_60(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_76(x))
Eq(F_62(x), F_6(x) + F_63(x))
Eq(F_63(x), F_28(x) + F_64(x) + F_69(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_10(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_12(x) + F_66(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_68(x) + F_71(x))
Eq(F_71(x), F_72(x) + F_74(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), x**2)
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_12(x)*F_71(x))
Eq(F_76(x), F_59(x) + F_77(x))
Eq(F_77(x), F_100(x) + F_122(x) + F_28(x) + F_78(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_84(x))
Eq(F_80(x), F_63(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_66(x))
Eq(F_84(x), F_77(x) + F_85(x))
Eq(F_85(x), 2*F_28(x) + F_86(x) + F_90(x) + F_99(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_81(x))
Eq(F_89(x), F_85(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), 2*F_28(x) + F_93(x) + F_97(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_66(x))
Eq(F_96(x), F_92(x))
Eq(F_97(x), F_12(x)*F_98(x))
Eq(F_98(x), F_43(x) + F_92(x))
Eq(F_99(x), 0)
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_102(x) + F_92(x))
Eq(F_102(x), F_103(x) + F_120(x) + F_28(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x) + F_107(x))
Eq(F_105(x), F_10(x) + F_106(x))
Eq(F_106(x), F_28(x) + F_64(x) + F_67(x))
Eq(F_107(x), F_102(x) + F_108(x))
Eq(F_108(x), F_100(x) + F_109(x) + F_28(x) + F_97(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_106(x) + F_112(x))
Eq(F_112(x), F_82(x))
Eq(F_113(x), F_108(x) + F_114(x))
Eq(F_114(x), F_115(x) + F_119(x) + 2*F_28(x) + F_90(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_112(x))
Eq(F_118(x), F_114(x))
Eq(F_119(x), 0)
Eq(F_120(x), F_12(x)*F_121(x))
Eq(F_121(x), F_102(x) + F_20(x))
Eq(F_122(x), F_12(x)*F_123(x))
Eq(F_123(x), F_124(x) + F_98(x))
Eq(F_124(x), F_125(x) + F_127(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_12(x)*F_43(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_12(x)*F_124(x))
Eq(F_129(x), F_12(x)*F_130(x))
Eq(F_130(x), F_121(x) + F_131(x))
Eq(F_131(x), F_132(x) + F_134(x))
Eq(F_132(x), F_133(x) + F_28(x) + F_44(x))
Eq(F_133(x), F_12(x)*F_58(x))
Eq(F_134(x), F_135(x) + 2*F_28(x) + F_93(x))
Eq(F_135(x), F_12(x)*F_131(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": [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]]}], "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": [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]]}], "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": [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]]}], "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": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 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, 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": [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]]}], "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, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 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": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": 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