0132_1203_3120
Counting sequence:
1, 1, 2, 6, 21, 73, 239, 734, 2131, 5900, 15697, 40389, 101047, 246915, 591507, 1393504, 3236723, 7427942, 16871397, 37981615, 84849047, 188275845, 415305591, 911297410, 1990300115, 4328645552, 9378611833, 20250275753, 43587415255, 93550001079, 200253136411, 427618014708, 911070324051, 1937030696554, 4110284215181, 8705899296563, 18408230501367, 38860864857241, 81913617134591, 172417168108854, 362426521408371, 760862047660564, 1595391373292705, 3341415838365389, 6990694931133559, 14610310511817131, 30504850603160227, 63630936925027272, 132609898405433779, 276126952156051758, 574490427469641525, 1194298326186823927, 2480920444731575255, 5149866173902384493, 10682538316127435655, 22144199367785774122, 45873665804401374611, 94971908941995011640, 196501058941435997385, 406332772779882706993, 839759200918019839895, 1734570403681009586783, 3580974193308875698219, 7389073923025291983068, 15239316447893313811603, 31414805157527377701810, 64729624954646828787421, 133314619420698942615291, 274450658328650723003703, 564765516560691647367937, 1161702154785932738753039, 2388631996616502436990046, 4909490254753354923844659, 10086974807409562196296732, 20717021760349133573682929, 42534354911206894462388181, 87297666802328261444518455, 179109915962279903690781139, 367362333435395440491225779, 753236343483639890194506032, 1543949387375333284777605619, 3163758869931484550238976502, 6481051318954027005634752133, 13272796573549013709136176447, 27174234573297634589084724247, 55620259108829859069923381589, 113813112361799649023582315415, 232829441451220662015058489810, 476181373236367056366715571027, 973639840897951586208213319616, 1990298098161070136969122012953, 4067561484081938238249855515065, 8310910453742400475535331762263, 16977109698759705089966654219271, 34672224620304930739374739347003, 70795314966652327160931187820740, 144522071946332434812823433874899, 294966449040606128860764206495738, 601896350620866172698153474185773, 1227957290808582968362337773995971, 2504719129725952768682298538087543
Generating function in Maple syntax:
-(x^9+13*x^8-80*x^7+193*x^6-274*x^5+248*x^4-145*x^3+53*x^2-11*x+1)/(2*x-1)^3/(-1+x)^6
Generating function in latex syntax:
-\frac{x^{9}+13 x^{8}-80 x^{7}+193 x^{6}-274 x^{5}+248 x^{4}-145 x^{3}+53 x^{2}-11 x +1}{\left(2 x -1\right)^{3} \left(-1+x \right)^{6}}
Generating function in sympy syntax:
(-x**9 - 13*x**8 + 80*x**7 - 193*x**6 + 274*x**5 - 248*x**4 + 145*x**3 - 53*x**2 + 11*x - 1)/((x - 1)**6*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^3*(-1+x)^6*F(x)+x^9+13*x^8-80*x^7+193*x^6-274*x^5+248*x^4-145*x^3+53*x^2-11*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{3} \left(-1+x \right)^{6} F \! \left(x \right)+x^{9}+13 x^{8}-80 x^{7}+193 x^{6}-274 x^{5}+248 x^{4}-145 x^{3}+53 x^{2}-11 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/240*(45*n^2+285*n-4290)*2^n+1/120*n^5+1/12*n^4+11/24*n^3+47/12*n^2+158/15*n+19)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(45 n^{2}+285 n -4290\right) 2^{n}}{240}+\frac{n^{5}}{120}+\frac{n^{4}}{12}+\frac{11 n^{3}}{24}+\frac{47 n^{2}}{12}+\frac{158 n}{15}+19 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 239
a(7) = 734
a(8) = 2131
a(9) = 5900
a(n+3) = -1/120*n^5+1/24*n^4+7/24*n^3-49/24*n^2+6*a(n+2)+8*a(n)-12*a(n+1)+343/60*n-3, n >= 10
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) = 73
a \! \left(6\right) = 239
a \! \left(7\right) = 734
a \! \left(8\right) = 2131
a \! \left(9\right) = 5900
a \! \left(n +3\right) = -\frac{n^{5}}{120}+\frac{n^{4}}{24}+\frac{7 n^{3}}{24}-\frac{49 n^{2}}{24}+6 a \! \left(n +2\right)+8 a \! \left(n \right)-12 a \! \left(n +1\right)+\frac{343 n}{60}-3, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14721/
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[29,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[23,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[9,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[10,x]
F[22,x] = F[18,x]
F[23,x] = F[24,x]+F[25,x]+F[28,x]
F[24,x] = 0
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[21,x]+F[27,x]
F[27,x] = F[23,x]
F[28,x] = F[12,x]*F[13,x]
F[29,x] = F[30,x]+F[40,x]
F[30,x] = F[31,x]
F[31,x] = F[12,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[1,x]+F[14,x]
F[34,x] = F[30,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[14,x]
F[39,x] = F[35,x]
F[40,x] = F[112,x]+F[24,x]+F[41,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]+F[62,x]
F[43,x] = F[44,x]+F[6,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[14,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[12,x]*F[47,x]
F[50,x] = F[51,x]+F[56,x]
F[51,x] = F[52,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[14,x]
F[55,x] = F[51,x]
F[56,x] = 2*F[24,x]+F[57,x]+F[61,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[48,x]
F[60,x] = F[56,x]
F[61,x] = F[12,x]*F[50,x]
F[62,x] = F[40,x]+F[63,x]
F[63,x] = 2*F[24,x]+F[64,x]+F[68,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[44,x]
F[67,x] = F[63,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[70,x]+F[77,x]
F[70,x] = F[35,x]+F[71,x]
F[71,x] = 2*F[24,x]+F[72,x]+F[76,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[48,x]
F[75,x] = F[71,x]
F[76,x] = F[12,x]*F[70,x]
F[77,x] = F[78,x]+F[92,x]
F[78,x] = 2*F[24,x]+F[79,x]+F[88,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[51,x]
F[82,x] = F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[51,x]
F[87,x] = F[83,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[35,x]
F[91,x] = F[78,x]
F[92,x] = 2*F[24,x]+F[107,x]+F[111,x]+F[93,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[95,x]+F[99,x]
F[95,x] = F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[12,x]*F[98,x]
F[98,x] = F[51,x]+F[96,x]
F[99,x] = F[100,x]
F[100,x] = 3*F[24,x]+F[101,x]+F[105,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[96,x]
F[104,x] = F[100,x]
F[105,x] = F[106,x]*F[12,x]
F[106,x] = F[100,x]+F[83,x]
F[107,x] = F[108,x]*F[12,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[71,x]
F[110,x] = F[92,x]
F[111,x] = F[12,x]*F[77,x]
F[112,x] = F[113,x]*F[12,x]
F[113,x] = F[114,x]+F[121,x]
F[114,x] = F[115,x]+F[30,x]
F[115,x] = F[116,x]+F[120,x]+F[24,x]
F[116,x] = F[117,x]*F[12,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[10,x]+F[48,x]
F[119,x] = F[115,x]+F[71,x]
F[120,x] = F[114,x]*F[12,x]
F[121,x] = F[122,x]+F[141,x]
F[122,x] = F[123,x]+F[127,x]+F[24,x]
F[123,x] = F[12,x]*F[124,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[14,x]+F[51,x]
F[126,x] = F[35,x]+F[83,x]
F[127,x] = F[12,x]*F[128,x]
F[128,x] = F[129,x]+F[135,x]
F[129,x] = F[130,x]+F[30,x]
F[130,x] = F[131,x]
F[131,x] = F[12,x]*F[132,x]
F[132,x] = F[133,x]+F[134,x]
F[133,x] = F[10,x]
F[134,x] = F[130,x]
F[135,x] = F[122,x]+F[136,x]
F[136,x] = F[137,x]
F[137,x] = F[12,x]*F[138,x]
F[138,x] = F[139,x]+F[140,x]
F[139,x] = F[130,x]
F[140,x] = F[136,x]
F[141,x] = F[142,x]+F[146,x]+F[150,x]+F[24,x]
F[142,x] = F[12,x]*F[143,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[48,x]+F[96,x]
F[145,x] = F[100,x]+F[71,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = F[115,x]
F[149,x] = F[141,x]
F[150,x] = F[12,x]*F[121,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_{29}\! \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_{23}\! \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_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \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_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{10}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{40}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \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_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{112}\! \left(x \right)+F_{24}\! \left(x \right)+F_{41}\! \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_{62}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{6}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{56}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{14}\! \left(x \right)
F_{55}\! \left(x \right) = F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{48}\! \left(x \right)
F_{60}\! \left(x \right) = F_{56}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{62}\! \left(x \right) = F_{40}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{44}\! \left(x \right)
F_{67}\! \left(x \right) = F_{63}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{77}\! \left(x \right)
F_{70}\! \left(x \right) = F_{35}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{72}\! \left(x \right)+F_{76}\! \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_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{48}\! \left(x \right)
F_{75}\! \left(x \right) = F_{71}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{92}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{79}\! \left(x \right)+F_{88}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{51}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{51}\! \left(x \right)
F_{87}\! \left(x \right) = F_{83}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{35}\! \left(x \right)
F_{91}\! \left(x \right) = F_{78}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{107}\! \left(x \right)+F_{111}\! \left(x \right)+F_{93}\! \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_{99}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{51}\! \left(x \right)+F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = 3 F_{24}\! \left(x \right)+F_{101}\! \left(x \right)+F_{105}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{96}\! \left(x \right)
F_{104}\! \left(x \right) = F_{100}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{100}\! \left(x \right)+F_{83}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{12}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{71}\! \left(x \right)
F_{110}\! \left(x \right) = F_{92}\! \left(x \right)
F_{111}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{12}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{121}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{30}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{120}\! \left(x \right)+F_{24}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{10}\! \left(x \right)+F_{48}\! \left(x \right)
F_{119}\! \left(x \right) = F_{115}\! \left(x \right)+F_{71}\! \left(x \right)
F_{120}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{141}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{127}\! \left(x \right)+F_{24}\! \left(x \right)
F_{123}\! \left(x \right) = F_{12}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{14}\! \left(x \right)+F_{51}\! \left(x \right)
F_{126}\! \left(x \right) = F_{35}\! \left(x \right)+F_{83}\! \left(x \right)
F_{127}\! \left(x \right) = F_{12}\! \left(x \right) F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{135}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{30}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{134}\! \left(x \right)
F_{133}\! \left(x \right) = F_{10}\! \left(x \right)
F_{134}\! \left(x \right) = F_{130}\! \left(x \right)
F_{135}\! \left(x \right) = F_{122}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{12}\! \left(x \right) F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{140}\! \left(x \right)
F_{139}\! \left(x \right) = F_{130}\! \left(x \right)
F_{140}\! \left(x \right) = F_{136}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{146}\! \left(x \right)+F_{150}\! \left(x \right)+F_{24}\! \left(x \right)
F_{142}\! \left(x \right) = F_{12}\! \left(x \right) F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{48}\! \left(x \right)+F_{96}\! \left(x \right)
F_{145}\! \left(x \right) = F_{100}\! \left(x \right)+F_{71}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = F_{115}\! \left(x \right)
F_{149}\! \left(x \right) = F_{141}\! \left(x \right)
F_{150}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \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_29(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_23(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_9(x))
Eq(F_17(x), F_14(x) + F_18(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_22(x))
Eq(F_21(x), F_10(x))
Eq(F_22(x), F_18(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_28(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_21(x) + F_27(x))
Eq(F_27(x), F_23(x))
Eq(F_28(x), F_12(x)*F_13(x))
Eq(F_29(x), F_30(x) + F_40(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_12(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_1(x) + F_14(x))
Eq(F_34(x), F_30(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_14(x))
Eq(F_39(x), F_35(x))
Eq(F_40(x), F_112(x) + F_24(x) + F_41(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_62(x))
Eq(F_43(x), F_44(x) + F_6(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_14(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_12(x)*F_47(x))
Eq(F_50(x), F_51(x) + F_56(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_14(x))
Eq(F_55(x), F_51(x))
Eq(F_56(x), 2*F_24(x) + F_57(x) + F_61(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_48(x))
Eq(F_60(x), F_56(x))
Eq(F_61(x), F_12(x)*F_50(x))
Eq(F_62(x), F_40(x) + F_63(x))
Eq(F_63(x), 2*F_24(x) + F_64(x) + F_68(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_44(x))
Eq(F_67(x), F_63(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_77(x))
Eq(F_70(x), F_35(x) + F_71(x))
Eq(F_71(x), 2*F_24(x) + F_72(x) + F_76(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_48(x))
Eq(F_75(x), F_71(x))
Eq(F_76(x), F_12(x)*F_70(x))
Eq(F_77(x), F_78(x) + F_92(x))
Eq(F_78(x), 2*F_24(x) + F_79(x) + F_88(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_51(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_51(x))
Eq(F_87(x), F_83(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_35(x))
Eq(F_91(x), F_78(x))
Eq(F_92(x), F_107(x) + F_111(x) + 2*F_24(x) + F_93(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_99(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_12(x)*F_98(x))
Eq(F_98(x), F_51(x) + F_96(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x) + F_105(x) + 3*F_24(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_96(x))
Eq(F_104(x), F_100(x))
Eq(F_105(x), F_106(x)*F_12(x))
Eq(F_106(x), F_100(x) + F_83(x))
Eq(F_107(x), F_108(x)*F_12(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_71(x))
Eq(F_110(x), F_92(x))
Eq(F_111(x), F_12(x)*F_77(x))
Eq(F_112(x), F_113(x)*F_12(x))
Eq(F_113(x), F_114(x) + F_121(x))
Eq(F_114(x), F_115(x) + F_30(x))
Eq(F_115(x), F_116(x) + F_120(x) + F_24(x))
Eq(F_116(x), F_117(x)*F_12(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_10(x) + F_48(x))
Eq(F_119(x), F_115(x) + F_71(x))
Eq(F_120(x), F_114(x)*F_12(x))
Eq(F_121(x), F_122(x) + F_141(x))
Eq(F_122(x), F_123(x) + F_127(x) + F_24(x))
Eq(F_123(x), F_12(x)*F_124(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_14(x) + F_51(x))
Eq(F_126(x), F_35(x) + F_83(x))
Eq(F_127(x), F_12(x)*F_128(x))
Eq(F_128(x), F_129(x) + F_135(x))
Eq(F_129(x), F_130(x) + F_30(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_12(x)*F_132(x))
Eq(F_132(x), F_133(x) + F_134(x))
Eq(F_133(x), F_10(x))
Eq(F_134(x), F_130(x))
Eq(F_135(x), F_122(x) + F_136(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_12(x)*F_138(x))
Eq(F_138(x), F_139(x) + F_140(x))
Eq(F_139(x), F_130(x))
Eq(F_140(x), F_136(x))
Eq(F_141(x), F_142(x) + F_146(x) + F_150(x) + F_24(x))
Eq(F_142(x), F_12(x)*F_143(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_48(x) + F_96(x))
Eq(F_145(x), F_100(x) + F_71(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), F_115(x))
Eq(F_149(x), F_141(x))
Eq(F_150(x), F_12(x)*F_121(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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 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], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 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