0123_1032_1320
Counting sequence:
1, 1, 2, 6, 21, 71, 220, 646, 1835, 5095, 13924, 37627, 100859, 268756, 713023, 1885543, 4974068, 13097587, 34440547, 90467764, 237450167, 622857583, 1633072276, 4280258635, 11215502411, 29381846164, 76961231215, 201564237751, 527856262580, 1382254111075, 3619405192819, 9476959711732, 24813470431079, 64967444558911, 170096849200468, 445339074952123, 1165952319475163, 3052581771111892, 7991920769137567, 20923436086854919, 54778898592535412, 143414281892967763, 375465991490800771, 982987781388300340, 2573505530291831831, 6737545164722658319, 17639162674347069460, 46180008279260402731, 120900993005317844075, 316523232420460540180, 828669227623598597839, 2169485497185404896087, 5679789357402755375924, 14869886761963139802691, 38929879302367221174163, 101919767892899638003828, 266829457871853921405383, 698568672713706583348447, 1828876694251354742912212, 4788061678004535473932699, 12535308875690607335974907, 32817866020923997848170068, 85918291330794808836891391, 224937012258887273919216295, 588892754020720703434181876, 1541741266952982217410178099, 4036331081137640710850049955, 10567252045058769439247366836, 27665425191236326655106840695, 72429023803045528622502735535, 189621646766690895405260526484, 496435917594608429978997165067, 1299686108212296939303167611019, 3402622411432607477473378952596, 8908181134866175672202715815983, 23321921010727219897306261633783, 61057581932438084736059055362228, 159850824856832235743556877006627, 418494892778549025359983520765107, 1095633853759795646067137575503604, 2868406669062799524302916986175527, 7509586154552526149764588943882623, 19660351796842625370836800967191636, 51471469240471042854437716201130875, 134754055933561888975860152123078171, 352790698578197395639910349141858004, 923618039836995841077406113250004575, 2418063421004721213859378426503173191, 6330572223321029973034870038049549940, 16573653249246093050313513431225546515, 43390387524992697868042233742787229379, 113597509326882897934086314771456421172, 297402140457957790694762964520222593239, 778608912051594063671295086686492476751, 2038424595706031579361307311333817073428, 5336664875084915032496996878904083216363, 13971570029585542234298423388556681521323, 36578045213745369102735753413122459238932, 95762565611797879938583797103523691978127, 250709651621942900442365558402874608260759, 656366389254620080847212719115952115934772
Generating function in Maple syntax:
-(x^9-2*x^8-x^7+4*x^6-x^5-2*x^4+3*x^3-8*x^2+5*x-1)/(x-1)/(2*x-1)/(x^2-3*x+1)
Generating function in latex syntax:
-\frac{x^{9}-2 x^{8}-x^{7}+4 x^{6}-x^{5}-2 x^{4}+3 x^{3}-8 x^{2}+5 x -1}{\left(x -1\right) \left(2 x -1\right) \left(x^{2}-3 x +1\right)}
Generating function in sympy syntax:
(-x**9 + 2*x**8 + x**7 - 4*x**6 + x**5 + 2*x**4 - 3*x**3 + 8*x**2 - 5*x + 1)/((x - 1)*(2*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(2*x-1)*(x^2-3*x+1)*F(x)+x^9-2*x^8-x^7+4*x^6-x^5-2*x^4+3*x^3-8*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(2 x -1\right) \left(x^{2}-3 x +1\right) F \! \left(x \right)+x^{9}-2 x^{8}-x^{7}+4 x^{6}-x^{5}-2 x^{4}+3 x^{3}-8 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
-1/2*piecewise(n = 0,2569/32,n = 1,489/16,n = 2,89/8,n = 3,17/4,n = 4,5/2,n = 5,1,0)+2+87/10*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)-87/10*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)+41/2*(3/2+1/2*5^(1/2))^(-n)-119/64*2^n+41/2*(3/2-1/2*5^(1/2))^(-n)
Explicit closed form in latex syntax:
-\frac{\left(\left\{\begin{array}{cc}\frac{2569}{32} & n =0 \\ \frac{489}{16} & n =1 \\ \frac{89}{8} & n =2 \\ \frac{17}{4} & n =3 \\ \frac{5}{2} & n =4 \\ 1 & n =5 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)}{2}+2+\frac{87 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{10}-\frac{87 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{10}+\frac{41 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{2}-\frac{119 \,2^{n}}{64}+\frac{41 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{2}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 71
a(6) = 220
a(7) = 646
a(8) = 1835
a(9) = 5095
a(n+3) = 2*a(n)-7*a(n+1)+5*a(n+2)+2, 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) = 71
a \! \left(6\right) = 220
a \! \left(7\right) = 646
a \! \left(8\right) = 1835
a \! \left(9\right) = 5095
a \! \left(n +3\right) = 2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)+2, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14661/
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[5,x]
F[4,x] = x
F[5,x] = F[34,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]+F[16,x]+F[32,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]+F[4,x]
F[19,x] = F[20,x]
F[20,x] = F[11,x]*F[4,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[15,x]+F[16,x]+F[23,x]
F[23,x] = F[4,x]*F[7,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[4,x]
F[30,x] = F[31,x]
F[31,x] = F[27,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[26,x]+F[7,x]
F[34,x] = F[2,x]+F[35,x]
F[35,x] = F[141,x]+F[15,x]+F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[45,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[1,x]+F[4,x]
F[42,x] = F[15,x]+F[16,x]+F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[22,x]+F[7,x]
F[45,x] = F[131,x]+F[46,x]
F[46,x] = F[15,x]+F[36,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[2,x]+F[49,x]
F[49,x] = F[130,x]+F[15,x]+F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[22,x]+F[4,x]
F[53,x] = F[49,x]+F[54,x]
F[54,x] = F[120,x]+F[15,x]+F[55,x]+F[76,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[64,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[4,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[22,x]
F[64,x] = F[65,x]+F[68,x]
F[65,x] = 2*F[15,x]+F[55,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[49,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = 2*F[15,x]+F[72,x]+F[76,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[58,x]
F[75,x] = F[72,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[82,x]
F[80,x] = F[39,x]+F[81,x]
F[81,x] = F[27,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[78,x]
F[84,x] = 2*F[15,x]+F[115,x]+F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[92,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[59,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[31,x]
F[92,x] = F[119,x]+F[93,x]
F[93,x] = 2*F[15,x]+F[85,x]+F[94,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[31,x]+F[4,x]
F[100,x] = F[101,x]+F[96,x]
F[101,x] = 2*F[15,x]+F[102,x]+F[115,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[106,x]
F[104,x] = F[105,x]+F[58,x]
F[105,x] = F[90,x]
F[106,x] = F[107,x]+F[108,x]
F[107,x] = 2*F[15,x]+F[102,x]+F[94,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[114,x]
F[113,x] = F[58,x]
F[114,x] = F[111,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[96,x]
F[118,x] = F[111,x]
F[119,x] = F[109,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[126,x]
F[122,x] = F[123,x]+F[49,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[97,x]
F[126,x] = F[127,x]+F[71,x]
F[127,x] = F[128,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[111,x]
F[130,x] = F[2,x]*F[4,x]
F[131,x] = F[120,x]+F[132,x]+F[139,x]+F[15,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[136,x]
F[134,x] = F[135,x]+F[88,x]
F[135,x] = F[62,x]
F[136,x] = F[137,x]+F[138,x]
F[137,x] = 2*F[15,x]+F[132,x]+F[66,x]
F[138,x] = F[69,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[71,x]+F[77,x]
F[141,x] = F[142,x]*F[4,x]
F[142,x] = F[143,x]+F[147,x]
F[143,x] = F[144,x]+F[2,x]
F[144,x] = F[145,x]+F[15,x]+F[50,x]
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[125,x]+F[2,x]
F[147,x] = F[148,x]+F[77,x]
F[148,x] = 2*F[15,x]+F[149,x]+F[72,x]
F[149,x] = F[150,x]*F[4,x]
F[150,x] = F[129,x]+F[77,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{34}\! \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_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{32}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{141}\! \left(x \right)+F_{15}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{45}\! \left(x \right) = F_{131}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right)+F_{36}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{130}\! \left(x \right)+F_{15}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{22}\! \left(x \right)+F_{4}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{120}\! \left(x \right)+F_{15}\! \left(x \right)+F_{55}\! \left(x \right)+F_{76}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{64}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{22}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{55}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{49}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{72}\! \left(x \right)+F_{76}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \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_{58}\! \left(x \right)
F_{75}\! \left(x \right) = F_{72}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{39}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{27}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{78}\! \left(x \right)
F_{84}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{115}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{92}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{59}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{31}\! \left(x \right)
F_{92}\! \left(x \right) = F_{119}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{85}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \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_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{31}\! \left(x \right)+F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{102}\! \left(x \right)+F_{115}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{106}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{58}\! \left(x \right)
F_{105}\! \left(x \right) = F_{90}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)
F_{107}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{102}\! \left(x \right)+F_{94}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{114}\! \left(x \right)
F_{113}\! \left(x \right) = F_{58}\! \left(x \right)
F_{114}\! \left(x \right) = F_{111}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{96}\! \left(x \right)
F_{118}\! \left(x \right) = F_{111}\! \left(x \right)
F_{119}\! \left(x \right) = F_{109}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{126}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{49}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{125}\! \left(x \right) = F_{97}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{71}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{111}\! \left(x \right)
F_{130}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{120}\! \left(x \right)+F_{132}\! \left(x \right)+F_{139}\! \left(x \right)+F_{15}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{136}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{88}\! \left(x \right)
F_{135}\! \left(x \right) = F_{62}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{137}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{132}\! \left(x \right)+F_{66}\! \left(x \right)
F_{138}\! \left(x \right) = F_{69}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{147}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{2}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{15}\! \left(x \right)+F_{50}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{125}\! \left(x \right)+F_{2}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{77}\! \left(x \right)
F_{148}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{149}\! \left(x \right)+F_{72}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{129}\! \left(x \right)+F_{77}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_34(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_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_32(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x) + F_4(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_11(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_15(x) + F_16(x) + F_23(x))
Eq(F_23(x), F_4(x)*F_7(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_4(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_27(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_26(x) + F_7(x))
Eq(F_34(x), F_2(x) + F_35(x))
Eq(F_35(x), F_141(x) + F_15(x) + F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_45(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_1(x) + F_4(x))
Eq(F_42(x), F_15(x) + F_16(x) + F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_22(x) + F_7(x))
Eq(F_45(x), F_131(x) + F_46(x))
Eq(F_46(x), F_15(x) + F_36(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_2(x) + F_49(x))
Eq(F_49(x), F_130(x) + F_15(x) + F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_22(x) + F_4(x))
Eq(F_53(x), F_49(x) + F_54(x))
Eq(F_54(x), F_120(x) + F_15(x) + F_55(x) + F_76(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_64(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_4(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_22(x))
Eq(F_64(x), F_65(x) + F_68(x))
Eq(F_65(x), 2*F_15(x) + F_55(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_49(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), 2*F_15(x) + F_72(x) + F_76(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_58(x))
Eq(F_75(x), F_72(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_82(x))
Eq(F_80(x), F_39(x) + F_81(x))
Eq(F_81(x), F_27(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_78(x))
Eq(F_84(x), F_115(x) + 2*F_15(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_92(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_59(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_31(x))
Eq(F_92(x), F_119(x) + F_93(x))
Eq(F_93(x), 2*F_15(x) + F_85(x) + F_94(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_31(x) + F_4(x))
Eq(F_100(x), F_101(x) + F_96(x))
Eq(F_101(x), F_102(x) + F_115(x) + 2*F_15(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_106(x))
Eq(F_104(x), F_105(x) + F_58(x))
Eq(F_105(x), F_90(x))
Eq(F_106(x), F_107(x) + F_108(x))
Eq(F_107(x), F_102(x) + 2*F_15(x) + F_94(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_114(x))
Eq(F_113(x), F_58(x))
Eq(F_114(x), F_111(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_96(x))
Eq(F_118(x), F_111(x))
Eq(F_119(x), F_109(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_126(x))
Eq(F_122(x), F_123(x) + F_49(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_97(x))
Eq(F_126(x), F_127(x) + F_71(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_111(x))
Eq(F_130(x), F_2(x)*F_4(x))
Eq(F_131(x), F_120(x) + F_132(x) + F_139(x) + F_15(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_136(x))
Eq(F_134(x), F_135(x) + F_88(x))
Eq(F_135(x), F_62(x))
Eq(F_136(x), F_137(x) + F_138(x))
Eq(F_137(x), F_132(x) + 2*F_15(x) + F_66(x))
Eq(F_138(x), F_69(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_71(x) + F_77(x))
Eq(F_141(x), F_142(x)*F_4(x))
Eq(F_142(x), F_143(x) + F_147(x))
Eq(F_143(x), F_144(x) + F_2(x))
Eq(F_144(x), F_145(x) + F_15(x) + F_50(x))
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_125(x) + F_2(x))
Eq(F_147(x), F_148(x) + F_77(x))
Eq(F_148(x), F_149(x) + 2*F_15(x) + F_72(x))
Eq(F_149(x), F_150(x)*F_4(x))
Eq(F_150(x), F_129(x) + F_77(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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 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], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, 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