0123_0132_2301
Counting sequence:
1, 1, 2, 6, 21, 73, 238, 718, 2013, 5301, 13266, 31886, 74269, 168841, 376750, 828726, 1802901, 3888645, 8330626, 17749702, 37650245, 79565865, 167613006, 352122430, 737950765, 1543200757, 3220856082, 6710439582, 13958106957, 28990388585, 60128782030, 124553154790, 257696985253, 532574715525, 1099510198914, 2267741078550, 4672922511925, 9620724554569, 19791206796590, 40681927374126, 83562880468989, 171523810261429, 351843716742610, 721279623153454, 1477743622490109, 3025855993770441, 6192449481078126, 12666373944673046, 25895697849256501, 52917295612590469, 108086391046913794, 220676381730129894, 450359962724892837, 918734323970200809, 1873497444971425678, 3819052483994057374, 7782220156078563149, 15852670688324847093, 32281802128970651154, 65716525762567321150, 133738894534369266733, 272089475087188737193, 553402322211257084814, 1125251388496250715078, 2287396265139949834053, 4648579506574769637125, 9444732965739250074370, 19184613836657890157110, 38959523483674526122645, 79099638588066506866953, 160560460417567883016558, 325843287318005461485198, 661131307601750267413021, 1341152081134979173696693, 2720083094132915571353042, 5515724051991745532853198, 11182563831435319784004573, 22667359117774296938142217, 45939181145355908545366318, 93087288110326446352726774, 188592427859882151148011477, 382020558998222819094161157, 773712524553362671691775618, 1566767862220559410291479302, 3172221350668786954293358597, 6421813953792910175895248809, 12998370412496492886288132814, 26306225834814330841444587774, 53231421689271351820490977389, 107700783417828083916042434037, 217877446914226928382054018322, 440706653985595377863885428702, 891316828285473797927155201805, 1802440697199513680252898675177, 3644495475656159529302783037006, 7368219113826583396199335674022, 14894894552681695467585997364197, 30106701755420448285546421655941, 60847228810955011271841459614082, 122962108222138251945179901286998, 248459517644732962693353502591221
Generating function in Maple syntax:
-(12*x^7-36*x^6+78*x^5-98*x^4+75*x^3-35*x^2+9*x-1)/(2*x-1)^2/(x-1)^6
Generating function in latex syntax:
-\frac{12 x^{7}-36 x^{6}+78 x^{5}-98 x^{4}+75 x^{3}-35 x^{2}+9 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{6}}
Generating function in sympy syntax:
(-12*x**7 + 36*x**6 - 78*x**5 + 98*x**4 - 75*x**3 + 35*x**2 - 9*x + 1)/((x - 1)**6*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x-1)^6*F(x)+12*x^7-36*x^6+78*x^5-98*x^4+75*x^3-35*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)+12 x^{7}-36 x^{6}+78 x^{5}-98 x^{4}+75 x^{3}-35 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
5+2^(n+1)*n-4*2^n-2/3*n^3+5/12*n^2+1/5*n+1/12*n^4-1/30*n^5
Explicit closed form in latex syntax:
5+2^{n +1} n -4 \,2^{n}-\frac{2 n^{3}}{3}+\frac{5 n^{2}}{12}+\frac{n}{5}+\frac{n^{4}}{12}-\frac{n^{5}}{30}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 238
a(7) = 718
a(n+2) = -1/30*n^5+5/12*n^4-4/3*n^3+37/12*n^2-4*a(n)+4*a(n+1)-32/15*n+2, 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) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 238
a \! \left(7\right) = 718
a \! \left(n +2\right) = -\frac{n^{5}}{30}+\frac{5 n^{4}}{12}-\frac{4 n^{3}}{3}+\frac{37 n^{2}}{12}-4 a \! \left(n \right)+4 a \! \left(n +1\right)-\frac{32 n}{15}+2, \quad n \geq 8
Specification 1
Strategy pack name: insertion_point_placements
Tree: http://permpal.com/tree/230/
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[22,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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]+F[14,x]+F[18,x]
F[13,x] = 0
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[4,x]
F[17,x] = F[12,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[1,x]+F[20,x]
F[22,x] = F[2,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[103,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[23,x]+F[7,x]
F[28,x] = F[29,x]+F[55,x]
F[29,x] = F[30,x]+F[7,x]
F[30,x] = F[13,x]+F[31,x]+F[37,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[4,x]
F[34,x] = F[35,x]
F[35,x] = F[13,x]+F[31,x]+F[36,x]
F[36,x] = F[19,x]*F[4,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[43,x]
F[39,x] = F[19,x]+F[40,x]
F[40,x] = F[13,x]+F[36,x]+F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[4,x]+F[40,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[13,x]+F[37,x]+F[41,x]
F[45,x] = F[13,x]+F[46,x]+F[47,x]+F[51,x]
F[46,x] = 0
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[40,x]
F[50,x] = F[45,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[19,x]+F[52,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[19,x]*F[7,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[70,x]
F[60,x] = F[61,x]
F[61,x] = F[19,x]*F[21,x]*F[62,x]
F[62,x] = F[63,x]+F[68,x]
F[63,x] = F[19,x]+F[64,x]
F[64,x] = F[13,x]+F[65,x]+F[67,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[19,x]+F[64,x]
F[67,x] = F[4,x]*F[63,x]
F[68,x] = F[19,x]*F[69,x]
F[69,x] = F[21,x]+F[63,x]
F[70,x] = F[19,x]*F[71,x]
F[71,x] = F[60,x]+F[72,x]
F[72,x] = F[73,x]+F[98,x]
F[73,x] = F[74,x]+F[96,x]
F[74,x] = F[19,x]+F[75,x]
F[75,x] = F[13,x]+F[76,x]+F[78,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[7,x]+F[75,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[84,x]
F[80,x] = F[19,x]+F[81,x]
F[81,x] = F[13,x]+F[18,x]+F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[4,x]+F[81,x]
F[84,x] = F[75,x]+F[85,x]
F[85,x] = F[13,x]+F[86,x]+F[88,x]+F[92,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[12,x]+F[85,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[81,x]
F[91,x] = F[85,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[19,x]+F[93,x]
F[96,x] = F[97,x]
F[97,x] = F[19,x]^2*F[21,x]
F[98,x] = F[101,x]+F[99,x]
F[99,x] = F[100,x]*F[19,x]
F[100,x] = F[6,x]+F[74,x]
F[101,x] = F[102,x]
F[102,x] = F[21,x]^2*F[64,x]
F[103,x] = F[104,x]+F[132,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[19,x]*F[4,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[117,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[104,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[19,x]
F[113,x] = F[114,x]+F[116,x]+F[13,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[113,x]+F[19,x]
F[116,x] = F[112,x]*F[4,x]
F[117,x] = F[118,x]*F[19,x]
F[118,x] = F[119,x]+F[123,x]
F[119,x] = F[120,x]+F[20,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[12,x]+F[4,x]
F[122,x] = F[81,x]+F[85,x]
F[123,x] = F[111,x]+F[124,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[112,x]+F[127,x]
F[127,x] = F[113,x]+F[128,x]
F[128,x] = 2*F[13,x]+F[129,x]+F[131,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[128,x]+F[52,x]
F[131,x] = F[127,x]*F[4,x]
F[132,x] = F[133,x]+F[135,x]
F[133,x] = F[134,x]*F[19,x]
F[134,x] = F[35,x]+F[7,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[113,x]*F[7,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[140,x]*F[4,x]
F[139,x] = F[113,x]+F[127,x]
F[140,x] = F[141,x]+F[19,x]
F[141,x] = F[19,x]*F[21,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_{22}\! \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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = 0
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \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_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{103}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{55}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{7}\! \left(x \right)
F_{30}\! \left(x \right) = F_{13}\! \left(x \right)+F_{31}\! \left(x \right)+F_{37}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right)+F_{31}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{39}\! \left(x \right) = F_{19}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{13}\! \left(x \right)+F_{36}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right)+F_{46}\! \left(x \right)+F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{46}\! \left(x \right) = 0
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{40}\! \left(x \right)
F_{50}\! \left(x \right) = F_{45}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{19}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{70}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = F_{19}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{13}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{19}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{68}\! \left(x \right) = F_{19}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{21}\! \left(x \right)+F_{63}\! \left(x \right)
F_{70}\! \left(x \right) = F_{19}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{60}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{98}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{96}\! \left(x \right)
F_{74}\! \left(x \right) = F_{19}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{13}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{7}\! \left(x \right)+F_{75}\! \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_{84}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right)+F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{75}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{13}\! \left(x \right)+F_{86}\! \left(x \right)+F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \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_{81}\! \left(x \right)
F_{91}\! \left(x \right) = F_{85}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \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_{19}\! \left(x \right)+F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{21}\! \left(x \right)
F_{98}\! \left(x \right) = F_{101}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{19}\! \left(x \right)
F_{100}\! \left(x \right) = F_{6}\! \left(x \right)+F_{74}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{21} \left(x \right)^{2} F_{64}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{132}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{117}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{104}\! \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_{19}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{116}\! \left(x \right)+F_{13}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)+F_{19}\! \left(x \right)
F_{116}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{19}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{20}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{12}\! \left(x \right)+F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{81}\! \left(x \right)+F_{85}\! \left(x \right)
F_{123}\! \left(x \right) = F_{111}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{112}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{113}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{129}\! \left(x \right)+F_{131}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{128}\! \left(x \right)+F_{52}\! \left(x \right)
F_{131}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{135}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{19}\! \left(x \right)
F_{134}\! \left(x \right) = F_{35}\! \left(x \right)+F_{7}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{113}\! \left(x \right) F_{7}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{113}\! \left(x \right)+F_{127}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{19}\! \left(x \right)
F_{141}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \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_22(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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x) + F_14(x) + F_18(x))
Eq(F_13(x), 0)
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_4(x))
Eq(F_17(x), F_12(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_1(x) + F_20(x))
Eq(F_22(x), F_2(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_103(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_23(x) + F_7(x))
Eq(F_28(x), F_29(x) + F_55(x))
Eq(F_29(x), F_30(x) + F_7(x))
Eq(F_30(x), F_13(x) + F_31(x) + F_37(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_4(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_13(x) + F_31(x) + F_36(x))
Eq(F_36(x), F_19(x)*F_4(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_43(x))
Eq(F_39(x), F_19(x) + F_40(x))
Eq(F_40(x), F_13(x) + F_36(x) + F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_4(x) + F_40(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_13(x) + F_37(x) + F_41(x))
Eq(F_45(x), F_13(x) + F_46(x) + F_47(x) + F_51(x))
Eq(F_46(x), 0)
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_40(x))
Eq(F_50(x), F_45(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_19(x) + F_52(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_19(x)*F_7(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_70(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_19(x)*F_21(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_68(x))
Eq(F_63(x), F_19(x) + F_64(x))
Eq(F_64(x), F_13(x) + F_65(x) + F_67(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_19(x) + F_64(x))
Eq(F_67(x), F_4(x)*F_63(x))
Eq(F_68(x), F_19(x)*F_69(x))
Eq(F_69(x), F_21(x) + F_63(x))
Eq(F_70(x), F_19(x)*F_71(x))
Eq(F_71(x), F_60(x) + F_72(x))
Eq(F_72(x), F_73(x) + F_98(x))
Eq(F_73(x), F_74(x) + F_96(x))
Eq(F_74(x), F_19(x) + F_75(x))
Eq(F_75(x), F_13(x) + F_76(x) + F_78(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_7(x) + F_75(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_84(x))
Eq(F_80(x), F_19(x) + F_81(x))
Eq(F_81(x), F_13(x) + F_18(x) + F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_4(x) + F_81(x))
Eq(F_84(x), F_75(x) + F_85(x))
Eq(F_85(x), F_13(x) + F_86(x) + F_88(x) + F_92(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_12(x) + F_85(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_81(x))
Eq(F_91(x), F_85(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_19(x) + F_93(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_19(x)**2*F_21(x))
Eq(F_98(x), F_101(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_19(x))
Eq(F_100(x), F_6(x) + F_74(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_21(x)**2*F_64(x))
Eq(F_103(x), F_104(x) + F_132(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_19(x)*F_4(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_117(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_104(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_19(x))
Eq(F_113(x), F_114(x) + F_116(x) + F_13(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_113(x) + F_19(x))
Eq(F_116(x), F_112(x)*F_4(x))
Eq(F_117(x), F_118(x)*F_19(x))
Eq(F_118(x), F_119(x) + F_123(x))
Eq(F_119(x), F_120(x) + F_20(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_12(x) + F_4(x))
Eq(F_122(x), F_81(x) + F_85(x))
Eq(F_123(x), F_111(x) + F_124(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_112(x) + F_127(x))
Eq(F_127(x), F_113(x) + F_128(x))
Eq(F_128(x), F_129(x) + 2*F_13(x) + F_131(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_128(x) + F_52(x))
Eq(F_131(x), F_127(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_135(x))
Eq(F_133(x), F_134(x)*F_19(x))
Eq(F_134(x), F_35(x) + F_7(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_113(x)*F_7(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_140(x)*F_4(x))
Eq(F_139(x), F_113(x) + F_127(x))
Eq(F_140(x), F_141(x) + F_19(x))
Eq(F_141(x), F_19(x)*F_21(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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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