0132_0213_1230_2301_3012
Counting sequence:
1, 1, 2, 6, 19, 52, 125, 274, 567, 1136, 2241, 4398, 8635, 17004, 33605, 66634, 132479, 263912, 526473, 1051238, 2100355, 4198116, 8393101, 16782466, 33560519, 67115872, 134225745, 268444574, 536881227, 1073753436, 2147496661, 4294981818, 8589950735, 17179887064, 34359758105, 68719498454, 137438977299, 274877933012, 549755842333, 1099511658738, 2199023289175, 4398046547536, 8796093061601, 17592186086926, 35184372134619, 70368744226892, 140737488408165, 281474976767274, 562949953481887, 1125899906907336, 2251799813754281, 4503599627444038, 9007199254819235, 18014398509565124, 36028797019052205, 72057594038021474, 144115188075954919, 288230376151816512, 576460752303534193, 1152921504606963838, 2305843009213817195, 4611686018427517756, 9223372036854912501, 18446744073709695386, 36893488147419254319, 73786976294838365112, 147573952589676579385, 295147905179353000374, 590295810358705834547, 1180591620717411494836, 2361183241434822807101, 4722366482869645423058, 9444732965739290646135, 18889465931478581083184, 37778931862957161947905, 75557863725914323667694, 151115727451828647097339, 302231454903657293946412, 604462909807314587634053, 1208925819614629174998538, 2417851639229258349716415, 4835703278458516699140776, 9671406556917033397977801, 19342813113834066795639846, 38685626227668133590951619, 77371252455336267181562532, 154742504910672534362771405, 309485009821345068725175874, 618970019642690137449971207, 1237940039285380274899547936, 2475880078570760549798687121, 4951760157141521099596950878, 9903520314283042199193463435, 19807040628566084398386473244, 39614081257132168796772477205, 79228162514264337593544469114, 158456325028528675187088436559, 316912650057057350374176354712, 633825300114114700748352173913, 1267650600228229401496703794838, 2535301200456458802993407018835
Generating function in Maple syntax:
(2*x^7+x^6+3*x^5-4*x^4+8*x^3-10*x^2+5*x-1)/(2*x-1)/(x-1)^4
Generating function in latex syntax:
\frac{2 x^{7}+x^{6}+3 x^{5}-4 x^{4}+8 x^{3}-10 x^{2}+5 x -1}{\left(2 x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(2*x**7 + x**6 + 3*x**5 - 4*x**4 + 8*x**3 - 10*x**2 + 5*x - 1)/((x - 1)**4*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x-1)^4*F(x)+2*x^7+x^6+3*x^5-4*x^4+8*x^3-10*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x -1\right)^{4} F \! \left(x \right)+2 x^{7}+x^{6}+3 x^{5}-4 x^{4}+8 x^{3}-10 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,-17+2^(n+1)+2/3*n^3-6*n^2+43/3*n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ -17+2^{n +1}+\frac{2 n^{3}}{3}-6 n^{2}+\frac{43 n}{3} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 52
a(6) = 125
a(7) = 274
a(n+1) = -2/3*n^3+8*n^2+2*a(n)-73/3*n+26, 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) = 19
a \! \left(5\right) = 52
a \! \left(6\right) = 125
a \! \left(7\right) = 274
a \! \left(n +1\right) = -\frac{2 n^{3}}{3}+8 n^{2}+2 a \! \left(n \right)-\frac{73 n}{3}+26, \quad n \geq 8
Specification 1
Strategy pack name: insertion_point_placements
Tree: http://permpal.com/tree/21628/
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[8,x]
F[4,x] = F[27,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = 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[8,x]
F[13,x] = F[14,x]+F[24,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[8,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[8,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[8,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[8,x]
F[23,x] = F[1,x]+F[21,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[8,x]
F[26,x] = F[21,x]
F[27,x] = F[28,x]+F[49,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[8,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[1,x]+F[29,x]
F[32,x] = F[33,x]*F[8,x]
F[33,x] = F[23,x]+F[32,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[23,x]*F[36,x]*F[8,x]
F[36,x] = F[37,x]+F[44,x]
F[37,x] = F[23,x]+F[38,x]
F[38,x] = F[21,x]+F[39,x]
F[39,x] = F[40,x]+F[41,x]+F[43,x]
F[40,x] = 0
F[41,x] = F[42,x]*F[8,x]
F[42,x] = F[21,x]+F[39,x]
F[43,x] = F[38,x]*F[8,x]
F[44,x] = F[21,x]+F[45,x]
F[45,x] = F[40,x]+F[46,x]+F[47,x]
F[46,x] = F[44,x]*F[8,x]
F[47,x] = F[48,x]*F[8,x]
F[48,x] = F[21,x]+F[45,x]
F[49,x] = F[50,x]
F[50,x] = F[51,x]*F[8,x]
F[51,x] = F[52,x]+F[67,x]
F[52,x] = F[21,x]+F[53,x]
F[53,x] = F[40,x]+F[46,x]+F[54,x]
F[54,x] = F[55,x]*F[8,x]
F[55,x] = F[56,x]+F[60,x]
F[56,x] = F[21,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]*F[8,x]
F[59,x] = F[57,x]+F[8,x]
F[60,x] = F[53,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]*F[8,x]
F[63,x] = F[64,x]+F[66,x]
F[64,x] = F[65,x]
F[65,x] = F[21,x]*F[8,x]
F[66,x] = F[62,x]
F[67,x] = F[103,x]+F[68,x]
F[68,x] = F[69,x]+F[97,x]
F[69,x] = F[70,x]+F[79,x]
F[70,x] = F[71,x]
F[71,x] = F[72,x]*F[8,x]
F[72,x] = F[17,x]+F[73,x]
F[73,x] = F[70,x]+F[74,x]
F[74,x] = F[40,x]+F[65,x]+F[75,x]
F[75,x] = F[76,x]*F[8,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[8,x]
F[78,x] = F[74,x]
F[79,x] = F[40,x]+F[80,x]+F[95,x]
F[80,x] = F[8,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[11,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[11,x]*F[8,x]
F[85,x] = F[79,x]+F[86,x]
F[86,x] = 2*F[40,x]+F[87,x]+F[91,x]
F[87,x] = F[8,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[83,x]
F[90,x] = F[86,x]
F[91,x] = F[8,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[8,x]*F[94,x]
F[94,x] = F[11,x]+F[92,x]
F[95,x] = F[8,x]*F[96,x]
F[96,x] = F[21,x]+F[92,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[14,x]*F[21,x]
F[99,x] = F[100,x]*F[21,x]
F[100,x] = F[101,x]+F[40,x]+F[65,x]
F[101,x] = F[102,x]*F[8,x]
F[102,x] = F[100,x]+F[8,x]
F[103,x] = F[104,x]+F[121,x]
F[104,x] = F[105,x]+F[40,x]+F[43,x]
F[105,x] = F[106,x]*F[8,x]
F[106,x] = F[107,x]+F[111,x]
F[107,x] = F[108,x]+F[21,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[8,x]
F[110,x] = F[108,x]+F[8,x]
F[111,x] = F[104,x]+F[112,x]
F[112,x] = 2*F[40,x]+F[113,x]+F[117,x]
F[113,x] = F[114,x]*F[8,x]
F[114,x] = F[115,x]+F[116,x]
F[115,x] = F[108,x]
F[116,x] = F[112,x]
F[117,x] = F[118,x]*F[8,x]
F[118,x] = F[119,x]+F[120,x]
F[119,x] = F[20,x]
F[120,x] = F[117,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[8,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[121,x]+F[39,x]
F[125,x] = F[126,x]+F[138,x]
F[126,x] = F[127,x]+F[136,x]
F[127,x] = F[128,x]+F[134,x]
F[128,x] = F[129,x]+F[132,x]+F[40,x]
F[129,x] = F[130,x]*F[8,x]
F[130,x] = F[131,x]+F[8,x]
F[131,x] = F[129,x]+F[20,x]+F[40,x]
F[132,x] = F[133,x]*F[8,x]
F[133,x] = F[128,x]+F[21,x]
F[134,x] = F[135,x]
F[135,x] = F[21,x]^2*F[8,x]
F[136,x] = F[137,x]
F[137,x] = F[21,x]^3*F[17,x]
F[138,x] = F[139,x]+F[149,x]
F[139,x] = 2*F[40,x]+F[140,x]+F[143,x]
F[140,x] = F[141,x]*F[8,x]
F[141,x] = F[108,x]+F[142,x]
F[142,x] = 2*F[40,x]+F[117,x]+F[140,x]
F[143,x] = F[144,x]*F[8,x]
F[144,x] = F[145,x]+F[148,x]
F[145,x] = F[146,x]
F[146,x] = F[147,x]*F[8,x]
F[147,x] = F[145,x]+F[21,x]
F[148,x] = F[143,x]
F[149,x] = F[150,x]
F[150,x] = F[21,x]^2*F[45,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_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{27}\! \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_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
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_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{49}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{8}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right)+F_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{23}\! \left(x \right) F_{36}\! \left(x \right) F_{8}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{21}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{8}\! \left(x \right)
F_{42}\! \left(x \right) = F_{21}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right) F_{8}\! \left(x \right)
F_{44}\! \left(x \right) = F_{21}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{40}\! \left(x \right)+F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right) F_{8}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{8}\! \left(x \right)
F_{48}\! \left(x \right) = F_{21}\! \left(x \right)+F_{45}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right) F_{8}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{67}\! \left(x \right)
F_{52}\! \left(x \right) = F_{21}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{40}\! \left(x \right)+F_{46}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{21}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right) F_{8}\! \left(x \right)
F_{59}\! \left(x \right) = F_{57}\! \left(x \right)+F_{8}\! \left(x \right)
F_{60}\! \left(x \right) = F_{53}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{8}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{21}\! \left(x \right) F_{8}\! \left(x \right)
F_{66}\! \left(x \right) = F_{62}\! \left(x \right)
F_{67}\! \left(x \right) = F_{103}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{97}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{79}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right) F_{8}\! \left(x \right)
F_{72}\! \left(x \right) = F_{17}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{70}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{40}\! \left(x \right)+F_{65}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right) F_{8}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{8}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{40}\! \left(x \right)+F_{80}\! \left(x \right)+F_{95}\! \left(x \right)
F_{80}\! \left(x \right) = F_{8}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{11}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{85}\! \left(x \right) = F_{79}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{40}\! \left(x \right)+F_{87}\! \left(x \right)+F_{91}\! \left(x \right)
F_{87}\! \left(x \right) = F_{8}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{83}\! \left(x \right)
F_{90}\! \left(x \right) = F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{8}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{8}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{11}\! \left(x \right)+F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{8}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{21}\! \left(x \right)+F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right) F_{21}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{21}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{40}\! \left(x \right)+F_{65}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{8}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right)+F_{8}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{121}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{8}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{21}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{8}\! \left(x \right)
F_{110}\! \left(x \right) = F_{108}\! \left(x \right)+F_{8}\! \left(x \right)
F_{111}\! \left(x \right) = F_{104}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{40}\! \left(x \right)+F_{113}\! \left(x \right)+F_{117}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{8}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)
F_{115}\! \left(x \right) = F_{108}\! \left(x \right)
F_{116}\! \left(x \right) = F_{112}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{8}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{120}\! \left(x \right)
F_{119}\! \left(x \right) = F_{20}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{8}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{121}\! \left(x \right)+F_{39}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{138}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{136}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{134}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{132}\! \left(x \right)+F_{40}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{8}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{8}\! \left(x \right)
F_{131}\! \left(x \right) = F_{129}\! \left(x \right)+F_{20}\! \left(x \right)+F_{40}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{8}\! \left(x \right)
F_{133}\! \left(x \right) = F_{128}\! \left(x \right)+F_{21}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{21} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{21} \left(x \right)^{3} F_{17}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{149}\! \left(x \right)
F_{139}\! \left(x \right) = 2 F_{40}\! \left(x \right)+F_{140}\! \left(x \right)+F_{143}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{8}\! \left(x \right)
F_{141}\! \left(x \right) = F_{108}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = 2 F_{40}\! \left(x \right)+F_{117}\! \left(x \right)+F_{140}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{8}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{148}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{8}\! \left(x \right)
F_{147}\! \left(x \right) = F_{145}\! \left(x \right)+F_{21}\! \left(x \right)
F_{148}\! \left(x \right) = F_{143}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{21} \left(x \right)^{2} F_{45}\! \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_8(x))
Eq(F_4(x), F_27(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_8(x)*F_9(x))
Eq(F_8(x), 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_8(x))
Eq(F_13(x), F_14(x) + F_24(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_8(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_8(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_8(x))
Eq(F_23(x), F_1(x) + F_21(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_8(x))
Eq(F_26(x), F_21(x))
Eq(F_27(x), F_28(x) + F_49(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_8(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_1(x) + F_29(x))
Eq(F_32(x), F_33(x)*F_8(x))
Eq(F_33(x), F_23(x) + F_32(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_23(x)*F_36(x)*F_8(x))
Eq(F_36(x), F_37(x) + F_44(x))
Eq(F_37(x), F_23(x) + F_38(x))
Eq(F_38(x), F_21(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_41(x) + F_43(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_42(x)*F_8(x))
Eq(F_42(x), F_21(x) + F_39(x))
Eq(F_43(x), F_38(x)*F_8(x))
Eq(F_44(x), F_21(x) + F_45(x))
Eq(F_45(x), F_40(x) + F_46(x) + F_47(x))
Eq(F_46(x), F_44(x)*F_8(x))
Eq(F_47(x), F_48(x)*F_8(x))
Eq(F_48(x), F_21(x) + F_45(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_51(x)*F_8(x))
Eq(F_51(x), F_52(x) + F_67(x))
Eq(F_52(x), F_21(x) + F_53(x))
Eq(F_53(x), F_40(x) + F_46(x) + F_54(x))
Eq(F_54(x), F_55(x)*F_8(x))
Eq(F_55(x), F_56(x) + F_60(x))
Eq(F_56(x), F_21(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x)*F_8(x))
Eq(F_59(x), F_57(x) + F_8(x))
Eq(F_60(x), F_53(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x)*F_8(x))
Eq(F_63(x), F_64(x) + F_66(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_21(x)*F_8(x))
Eq(F_66(x), F_62(x))
Eq(F_67(x), F_103(x) + F_68(x))
Eq(F_68(x), F_69(x) + F_97(x))
Eq(F_69(x), F_70(x) + F_79(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x)*F_8(x))
Eq(F_72(x), F_17(x) + F_73(x))
Eq(F_73(x), F_70(x) + F_74(x))
Eq(F_74(x), F_40(x) + F_65(x) + F_75(x))
Eq(F_75(x), F_76(x)*F_8(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_8(x))
Eq(F_78(x), F_74(x))
Eq(F_79(x), F_40(x) + F_80(x) + F_95(x))
Eq(F_80(x), F_8(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_11(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_11(x)*F_8(x))
Eq(F_85(x), F_79(x) + F_86(x))
Eq(F_86(x), 2*F_40(x) + F_87(x) + F_91(x))
Eq(F_87(x), F_8(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_83(x))
Eq(F_90(x), F_86(x))
Eq(F_91(x), F_8(x)*F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_8(x)*F_94(x))
Eq(F_94(x), F_11(x) + F_92(x))
Eq(F_95(x), F_8(x)*F_96(x))
Eq(F_96(x), F_21(x) + F_92(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_14(x)*F_21(x))
Eq(F_99(x), F_100(x)*F_21(x))
Eq(F_100(x), F_101(x) + F_40(x) + F_65(x))
Eq(F_101(x), F_102(x)*F_8(x))
Eq(F_102(x), F_100(x) + F_8(x))
Eq(F_103(x), F_104(x) + F_121(x))
Eq(F_104(x), F_105(x) + F_40(x) + F_43(x))
Eq(F_105(x), F_106(x)*F_8(x))
Eq(F_106(x), F_107(x) + F_111(x))
Eq(F_107(x), F_108(x) + F_21(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_8(x))
Eq(F_110(x), F_108(x) + F_8(x))
Eq(F_111(x), F_104(x) + F_112(x))
Eq(F_112(x), F_113(x) + F_117(x) + 2*F_40(x))
Eq(F_113(x), F_114(x)*F_8(x))
Eq(F_114(x), F_115(x) + F_116(x))
Eq(F_115(x), F_108(x))
Eq(F_116(x), F_112(x))
Eq(F_117(x), F_118(x)*F_8(x))
Eq(F_118(x), F_119(x) + F_120(x))
Eq(F_119(x), F_20(x))
Eq(F_120(x), F_117(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_8(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_121(x) + F_39(x))
Eq(F_125(x), F_126(x) + F_138(x))
Eq(F_126(x), F_127(x) + F_136(x))
Eq(F_127(x), F_128(x) + F_134(x))
Eq(F_128(x), F_129(x) + F_132(x) + F_40(x))
Eq(F_129(x), F_130(x)*F_8(x))
Eq(F_130(x), F_131(x) + F_8(x))
Eq(F_131(x), F_129(x) + F_20(x) + F_40(x))
Eq(F_132(x), F_133(x)*F_8(x))
Eq(F_133(x), F_128(x) + F_21(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_21(x)**2*F_8(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_17(x)*F_21(x)**3)
Eq(F_138(x), F_139(x) + F_149(x))
Eq(F_139(x), F_140(x) + F_143(x) + 2*F_40(x))
Eq(F_140(x), F_141(x)*F_8(x))
Eq(F_141(x), F_108(x) + F_142(x))
Eq(F_142(x), F_117(x) + F_140(x) + 2*F_40(x))
Eq(F_143(x), F_144(x)*F_8(x))
Eq(F_144(x), F_145(x) + F_148(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_147(x)*F_8(x))
Eq(F_147(x), F_145(x) + F_21(x))
Eq(F_148(x), F_143(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_21(x)**2*F_45(x))
Pack JSON:
{"expansion_strats": [[{"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}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": 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": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 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": [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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "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]]}], 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