0132_1203_1230_3120
Counting sequence:
1, 1, 2, 6, 20, 64, 192, 543, 1462, 3782, 9472, 23109, 55190, 129524, 299616, 684763, 1549158, 3474434, 7734448, 17106289, 37619270, 82315056, 179308592, 389024071, 840960630, 1811942334, 3892317472, 8338280093, 17817407542, 37983621612, 80799077312, 171530261939, 363461613510, 768799152634, 1623497645136, 3423088942793, 7206955131238, 15152644629544, 31817117738768, 66726611921439, 139775415692630, 292470093000886, 611328465056832, 1276532999862261, 2663017162488790, 5550334697029604, 11558066231198752, 24048518322735243, 49996992738250022, 103864266406253042, 215609832160384752, 447263737993255969, 927178573284925830, 1920785241073542944, 3976678470968175856, 8228076519205925623, 17014599392205764918, 35164105890508865454, 72634054790231393888, 149951853192928070989, 309415308798862595190, 638142052799889841116, 1315483436756412441472, 2710518457330697284451, 5582445925306353103750, 11492321557921050704874, 23648725902495645222032, 48644064122372087663993, 100018246367653188916902, 205570515957419243266072, 422356652311653893859792, 867439693322117955253199, 1780922459852214951280150, 3655111657741105395468454, 7499117974796996599419776, 15380747634706434461081253, 31535963372603490737138198, 64639752417519703685150164, 132452935111527808953827808, 271328288639758335398202939, 555652529840373934424414950, 1137599196257366053398603746, 2328391128577775790484190512, 4764376655101253577517138641, 9746359957733140406481293510, 19932768913806005832555536144, 40755307230848378737694715312, 83309496081283325687352114343, 170255441027967455932220296182, 347861151039191857246654028702, 710577582549808277792097430432, 1451175211052287027250498501629, 2963009484029557687971053964470, 6048575031948368023157121097164, 12344738071753812101294066904896, 25189603919378917833647379857683, 51389366910814705971612444939078, 104818859006371718636258646451674, 213757582463485182827381578168528, 435834121990968121102085270965289, 888464614434960281774001859239910
Generating function in Maple syntax:
(3*x^7-16*x^6+49*x^5-77*x^4+68*x^3-34*x^2+9*x-1)/(2*x-1)^3/(-1+x)^4
Generating function in latex syntax:
\frac{3 x^{7}-16 x^{6}+49 x^{5}-77 x^{4}+68 x^{3}-34 x^{2}+9 x -1}{\left(2 x -1\right)^{3} \left(-1+x \right)^{4}}
Generating function in sympy syntax:
(3*x**7 - 16*x**6 + 49*x**5 - 77*x**4 + 68*x**3 - 34*x**2 + 9*x - 1)/((x - 1)**4*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^3*(-1+x)^4*F(x)-3*x^7+16*x^6-49*x^5+77*x^4-68*x^3+34*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{3} \left(-1+x \right)^{4} F \! \left(x \right)-3 x^{7}+16 x^{6}-49 x^{5}+77 x^{4}-68 x^{3}+34 x^{2}-9 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/48*(3*n^2+39*n-258)*2^n+1/6*n^3+1/2*n^2+10/3*n+6)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(3 n^{2}+39 n -258\right) 2^{n}}{48}+\frac{n^{3}}{6}+\frac{n^{2}}{2}+\frac{10 n}{3}+6 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 192
a(7) = 543
a(n+3) = 8*a(n)-12*a(n+1)+6*a(n+2)-1/6*(n-3)*(n-2)*(n-1), n >= 8
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 192
a \! \left(7\right) = 543
a \! \left(n +3\right) = 8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)-\frac{\left(n -3\right) \left(n -2\right) \left(n -1\right)}{6}, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15547/
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[31,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[24,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[12,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]+F[26,x]+F[30,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[10,x]
F[29,x] = F[24,x]
F[30,x] = F[12,x]*F[13,x]
F[31,x] = F[32,x]+F[44,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[1,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[35,x]
F[38,x] = F[32,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[36,x]
F[43,x] = F[39,x]
F[44,x] = F[119,x]+F[25,x]+F[45,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[47,x]+F[66,x]
F[47,x] = F[48,x]+F[6,x]
F[48,x] = F[49,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[36,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[12,x]*F[51,x]
F[54,x] = F[55,x]+F[60,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[36,x]
F[59,x] = F[55,x]
F[60,x] = 2*F[25,x]+F[61,x]+F[65,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[52,x]
F[64,x] = F[60,x]
F[65,x] = F[12,x]*F[54,x]
F[66,x] = F[44,x]+F[67,x]
F[67,x] = 2*F[25,x]+F[68,x]+F[72,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[48,x]
F[71,x] = F[67,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[74,x]+F[81,x]
F[74,x] = F[39,x]+F[75,x]
F[75,x] = 2*F[25,x]+F[76,x]+F[80,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[52,x]
F[79,x] = F[75,x]
F[80,x] = F[12,x]*F[74,x]
F[81,x] = F[82,x]+F[99,x]
F[82,x] = 2*F[25,x]+F[83,x]+F[95,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[89,x]
F[85,x] = F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[36,x]+F[86,x]
F[89,x] = F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[86,x]
F[94,x] = F[90,x]
F[95,x] = F[12,x]*F[96,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[39,x]
F[98,x] = F[82,x]
F[99,x] = 2*F[25,x]+F[100,x]+F[114,x]+F[118,x]
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[102,x]+F[106,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[103,x]+F[86,x]
F[106,x] = F[107,x]
F[107,x] = 3*F[25,x]+F[108,x]+F[112,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[103,x]
F[111,x] = F[107,x]
F[112,x] = F[113,x]*F[12,x]
F[113,x] = F[107,x]+F[90,x]
F[114,x] = F[115,x]*F[12,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[75,x]
F[117,x] = F[99,x]
F[118,x] = F[12,x]*F[81,x]
F[119,x] = F[12,x]*F[120,x]
F[120,x] = F[121,x]+F[128,x]
F[121,x] = F[122,x]+F[32,x]
F[122,x] = F[123,x]+F[127,x]+F[25,x]
F[123,x] = F[12,x]*F[124,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[10,x]+F[52,x]
F[126,x] = F[122,x]+F[75,x]
F[127,x] = F[12,x]*F[121,x]
F[128,x] = F[129,x]+F[148,x]
F[129,x] = F[130,x]+F[134,x]+F[25,x]
F[130,x] = F[12,x]*F[131,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = F[36,x]+F[86,x]
F[133,x] = F[39,x]+F[90,x]
F[134,x] = F[12,x]*F[135,x]
F[135,x] = F[136,x]+F[142,x]
F[136,x] = F[137,x]+F[32,x]
F[137,x] = F[138,x]
F[138,x] = F[12,x]*F[139,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[12,x]
F[141,x] = F[137,x]
F[142,x] = F[129,x]+F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[12,x]*F[145,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[137,x]
F[147,x] = F[143,x]
F[148,x] = F[149,x]+F[153,x]+F[157,x]+F[25,x]
F[149,x] = F[12,x]*F[150,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[103,x]+F[52,x]
F[152,x] = F[107,x]+F[75,x]
F[153,x] = F[12,x]*F[154,x]
F[154,x] = F[155,x]+F[156,x]
F[155,x] = F[122,x]
F[156,x] = F[148,x]
F[157,x] = F[12,x]*F[128,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_{31}\! \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_{24}\! \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_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \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_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{10}\! \left(x \right)
F_{29}\! \left(x \right) = F_{24}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{44}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{32}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{36}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right)
F_{44}\! \left(x \right) = F_{119}\! \left(x \right)+F_{25}\! \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_{66}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{6}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{36}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{60}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{36}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{52}\! \left(x \right)
F_{64}\! \left(x \right) = F_{60}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{66}\! \left(x \right) = F_{44}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{68}\! \left(x \right)+F_{72}\! \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_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{48}\! \left(x \right)
F_{71}\! \left(x \right) = F_{67}\! \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_{81}\! \left(x \right)
F_{74}\! \left(x \right) = F_{39}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{52}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{99}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{83}\! \left(x \right)+F_{95}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{89}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{36}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{86}\! \left(x \right)
F_{94}\! \left(x \right) = F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{39}\! \left(x \right)
F_{98}\! \left(x \right) = F_{82}\! \left(x \right)
F_{99}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{100}\! \left(x \right)+F_{114}\! \left(x \right)+F_{118}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{86}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = 3 F_{25}\! \left(x \right)+F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{103}\! \left(x \right)
F_{111}\! \left(x \right) = F_{107}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{12}\! \left(x \right)
F_{113}\! \left(x \right) = F_{107}\! \left(x \right)+F_{90}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{75}\! \left(x \right)
F_{117}\! \left(x \right) = F_{99}\! \left(x \right)
F_{118}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{119}\! \left(x \right) = F_{12}\! \left(x \right) F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{128}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{32}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{127}\! \left(x \right)+F_{25}\! \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_{10}\! \left(x \right)+F_{52}\! \left(x \right)
F_{126}\! \left(x \right) = F_{122}\! \left(x \right)+F_{75}\! \left(x \right)
F_{127}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{148}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{134}\! \left(x \right)+F_{25}\! \left(x \right)
F_{130}\! \left(x \right) = F_{12}\! \left(x \right) F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = F_{36}\! \left(x \right)+F_{86}\! \left(x \right)
F_{133}\! \left(x \right) = F_{39}\! \left(x \right)+F_{90}\! \left(x \right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right) F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{142}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{32}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{12}\! \left(x \right) F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right)
F_{141}\! \left(x \right) = F_{137}\! \left(x \right)
F_{142}\! \left(x \right) = F_{129}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{137}\! \left(x \right)
F_{147}\! \left(x \right) = F_{143}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{153}\! \left(x \right)+F_{157}\! \left(x \right)+F_{25}\! \left(x \right)
F_{149}\! \left(x \right) = F_{12}\! \left(x \right) F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{103}\! \left(x \right)+F_{52}\! \left(x \right)
F_{152}\! \left(x \right) = F_{107}\! \left(x \right)+F_{75}\! \left(x \right)
F_{153}\! \left(x \right) = F_{12}\! \left(x \right) F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{156}\! \left(x \right)
F_{155}\! \left(x \right) = F_{122}\! \left(x \right)
F_{156}\! \left(x \right) = F_{148}\! \left(x \right)
F_{157}\! \left(x \right) = F_{12}\! \left(x \right) F_{128}\! \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_31(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_24(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_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_12(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_30(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_10(x))
Eq(F_29(x), F_24(x))
Eq(F_30(x), F_12(x)*F_13(x))
Eq(F_31(x), F_32(x) + F_44(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_1(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_35(x))
Eq(F_38(x), F_32(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_36(x))
Eq(F_43(x), F_39(x))
Eq(F_44(x), F_119(x) + F_25(x) + F_45(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_66(x))
Eq(F_47(x), F_48(x) + F_6(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_36(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_12(x)*F_51(x))
Eq(F_54(x), F_55(x) + F_60(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_36(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), 2*F_25(x) + F_61(x) + F_65(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_52(x))
Eq(F_64(x), F_60(x))
Eq(F_65(x), F_12(x)*F_54(x))
Eq(F_66(x), F_44(x) + F_67(x))
Eq(F_67(x), 2*F_25(x) + F_68(x) + F_72(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_48(x))
Eq(F_71(x), F_67(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_81(x))
Eq(F_74(x), F_39(x) + F_75(x))
Eq(F_75(x), 2*F_25(x) + F_76(x) + F_80(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_52(x))
Eq(F_79(x), F_75(x))
Eq(F_80(x), F_12(x)*F_74(x))
Eq(F_81(x), F_82(x) + F_99(x))
Eq(F_82(x), 2*F_25(x) + F_83(x) + F_95(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_89(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_36(x) + F_86(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_86(x))
Eq(F_94(x), F_90(x))
Eq(F_95(x), F_12(x)*F_96(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_39(x))
Eq(F_98(x), F_82(x))
Eq(F_99(x), F_100(x) + F_114(x) + F_118(x) + 2*F_25(x))
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_102(x) + F_106(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_103(x) + F_86(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x) + F_112(x) + 3*F_25(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_103(x))
Eq(F_111(x), F_107(x))
Eq(F_112(x), F_113(x)*F_12(x))
Eq(F_113(x), F_107(x) + F_90(x))
Eq(F_114(x), F_115(x)*F_12(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_75(x))
Eq(F_117(x), F_99(x))
Eq(F_118(x), F_12(x)*F_81(x))
Eq(F_119(x), F_12(x)*F_120(x))
Eq(F_120(x), F_121(x) + F_128(x))
Eq(F_121(x), F_122(x) + F_32(x))
Eq(F_122(x), F_123(x) + F_127(x) + F_25(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_10(x) + F_52(x))
Eq(F_126(x), F_122(x) + F_75(x))
Eq(F_127(x), F_12(x)*F_121(x))
Eq(F_128(x), F_129(x) + F_148(x))
Eq(F_129(x), F_130(x) + F_134(x) + F_25(x))
Eq(F_130(x), F_12(x)*F_131(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_36(x) + F_86(x))
Eq(F_133(x), F_39(x) + F_90(x))
Eq(F_134(x), F_12(x)*F_135(x))
Eq(F_135(x), F_136(x) + F_142(x))
Eq(F_136(x), F_137(x) + F_32(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_12(x)*F_139(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_12(x))
Eq(F_141(x), F_137(x))
Eq(F_142(x), F_129(x) + F_143(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_12(x)*F_145(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_137(x))
Eq(F_147(x), F_143(x))
Eq(F_148(x), F_149(x) + F_153(x) + F_157(x) + F_25(x))
Eq(F_149(x), F_12(x)*F_150(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_103(x) + F_52(x))
Eq(F_152(x), F_107(x) + F_75(x))
Eq(F_153(x), F_12(x)*F_154(x))
Eq(F_154(x), F_155(x) + F_156(x))
Eq(F_155(x), F_122(x))
Eq(F_156(x), F_148(x))
Eq(F_157(x), F_12(x)*F_128(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": [1, 2, 3, 0], "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": [1, 2, 3, 0], "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": [1, 2, 3, 0], "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], [0, 0]]}, {"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": [1, 2, 0, 3], "pos": [[0, 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