0132_1203_1230_1320_2301
Counting sequence:
1, 1, 2, 6, 19, 55, 143, 341, 765, 1650, 3479, 7256, 15083, 31377, 65431, 136791, 286521, 600756, 1259855, 2640802, 5530199, 11566635, 24158191, 50382985, 104921333, 218182214, 453080487, 939639900, 1946296259, 4026698069, 8321696423, 17180101995, 35433753457, 73014763176, 150324226335, 309238074630, 635655654575, 1305670625935, 2680060242239, 5497558879101, 11269995025453, 23089745135194, 47279001068855, 96757024453664, 197912094357147, 404620280541273, 826832745784631, 1688849862154559, 3448068466806953, 7036874420096988, 14355223814822767, 29273397580757034, 59672695065799431, 121597189942458675, 247697979509172239, 504403158269656369, 1026820715045027429, 2089670227104887214, 4251398048243178823, 8646911284557268900, 17582052945260853107, 35740566642819249053, 72634054790238946119, 147573952589684633043, 299759591197789108961, 608742554432424817232, 1235931852938550336575, 2508757194024510210318, 5091301364343848298847, 10330176681277361872407, 20955501267734064572511, 42501298345826821886373, 86183188312371041199005, 174727559866176890103874, 354177486215223409437143, 717799705396186092172008, 1454488876723850746859083, 2946756685310658635810593, 5969071234347231574075607, 12089258196146291772604199, 24480747847196240815003161, 49565958604199796191902212, 100340843028014221531395983, 203099537695257701383347122, 411034778668973919434830775, 831740963894864872234700091, 1682824740903563811230070319, 3404335108034795756013993177, 6886041468524927779170217941, 13926825441960528092661538326, 28163135893742401254004135655, 56945241807127492645411564012, 115128423653540365565673318179, 232732727385651491681093164773, 470417214928444504461728195047, 950737950171172051122591711547, 1921282940970910186643508563537, 3882179963198952542083724942072, 7843588088912169421760926218591, 15845632502852867518708869118998, 32008177655762792387791839065615
Generating function in Maple syntax:
-(x^8+5*x^7-35*x^6+76*x^5-96*x^4+75*x^3-35*x^2+9*x-1)/(2*x-1)^2/(x-1)^6
Generating function in latex syntax:
-\frac{x^{8}+5 x^{7}-35 x^{6}+76 x^{5}-96 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:
(-x**8 - 5*x**7 + 35*x**6 - 76*x**5 + 96*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)+x^8+5*x^7-35*x^6+76*x^5-96*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)+x^{8}+5 x^{7}-35 x^{6}+76 x^{5}-96 x^{4}+75 x^{3}-35 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1-13/10*n+1/2*n^2+1/120*n^5-5/24*n^3+1/4*2^n*n+1/4*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1-\frac{13 n}{10}+\frac{n^{2}}{2}+\frac{n^{5}}{120}-\frac{5 n^{3}}{24}+\frac{2^{n} n}{4}+\frac{2^{n}}{4} & \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) = 55
a(6) = 143
a(7) = 341
a(8) = 765
a(n+2) = 1/120*n^5-1/12*n^4-5/24*n^3+25/12*n^2+4*a(n+1)-4*a(n)-14/5*n+3, n >= 9
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) = 55
a \! \left(6\right) = 143
a \! \left(7\right) = 341
a \! \left(8\right) = 765
a \! \left(n +2\right) = \frac{n^{5}}{120}-\frac{n^{4}}{12}-\frac{5 n^{3}}{24}+\frac{25 n^{2}}{12}+4 a \! \left(n +1\right)-4 a \! \left(n \right)-\frac{14 n}{5}+3, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19831/
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[39,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[29,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[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[12,x]
F[24,x] = F[19,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[1,x]+F[26,x]
F[29,x] = F[20,x]+F[30,x]+F[34,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[10,x]
F[33,x] = F[29,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[26,x]+F[36,x]
F[36,x] = F[20,x]+F[34,x]+F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[10,x]+F[36,x]
F[39,x] = F[14,x]+F[40,x]
F[40,x] = F[116,x]+F[20,x]+F[41,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]+F[77,x]
F[43,x] = F[44,x]+F[6,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[12,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[12,x]*F[47,x]
F[50,x] = F[51,x]+F[67,x]
F[51,x] = F[52,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[57,x]
F[54,x] = F[12,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = x^2
F[57,x] = F[51,x]+F[58,x]
F[58,x] = 2*F[20,x]+F[59,x]+F[63,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[55,x]
F[62,x] = F[58,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[12,x]+F[64,x]
F[67,x] = 2*F[20,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[64,x]+F[74,x]
F[74,x] = 2*F[20,x]+F[72,x]+F[75,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[48,x]+F[74,x]
F[77,x] = F[40,x]+F[78,x]
F[78,x] = 2*F[20,x]+F[79,x]+F[83,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[44,x]
F[82,x] = F[78,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[87,x]
F[86,x] = F[25,x]
F[87,x] = F[88,x]
F[88,x] = F[12,x]*F[85,x]
F[89,x] = F[106,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[96,x]
F[93,x] = F[86,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[12,x]*F[86,x]
F[96,x] = F[90,x]+F[97,x]
F[97,x] = 3*F[20,x]+F[102,x]+F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[94,x]
F[101,x] = F[97,x]
F[102,x] = F[103,x]*F[12,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] = 3*F[20,x]+F[107,x]+F[111,x]
F[107,x] = F[108,x]*F[12,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[87,x]
F[110,x] = F[106,x]
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[103,x]+F[113,x]
F[113,x] = 3*F[20,x]+F[111,x]+F[114,x]
F[114,x] = F[115,x]*F[12,x]
F[115,x] = F[113,x]+F[87,x]
F[116,x] = F[117,x]*F[12,x]
F[117,x] = F[118,x]+F[35,x]
F[118,x] = F[119,x]+F[137,x]
F[119,x] = F[120,x]+F[123,x]+F[20,x]
F[120,x] = F[12,x]*F[121,x]
F[121,x] = F[12,x]+F[122,x]
F[122,x] = F[120,x]+F[20,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[122,x]+F[26,x]
F[126,x] = F[119,x]+F[127,x]
F[127,x] = F[128,x]+F[129,x]+F[133,x]+F[20,x]
F[128,x] = 0
F[129,x] = F[12,x]*F[130,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[122,x]
F[132,x] = F[127,x]
F[133,x] = F[12,x]*F[134,x]
F[134,x] = F[135,x]
F[135,x] = F[12,x]*F[136,x]
F[136,x] = F[134,x]+F[26,x]
F[137,x] = F[138,x]+F[141,x]+F[145,x]+F[20,x]
F[138,x] = F[12,x]*F[139,x]
F[139,x] = F[140,x]+F[48,x]
F[140,x] = 2*F[20,x]+F[138,x]+F[88,x]
F[141,x] = F[12,x]*F[142,x]
F[142,x] = F[143,x]+F[144,x]
F[143,x] = F[36,x]
F[144,x] = F[137,x]
F[145,x] = F[12,x]*F[146,x]
F[146,x] = F[134,x]+F[147,x]
F[147,x] = 2*F[20,x]+F[145,x]+F[148,x]
F[148,x] = F[12,x]*F[149,x]
F[149,x] = F[147,x]+F[36,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_{39}\! \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_{29}\! \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_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{20}\! \left(x \right)+F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{10}\! \left(x \right)
F_{33}\! \left(x \right) = F_{29}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{26}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{10}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{116}\! \left(x \right)+F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{77}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{6}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{67}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = x^{2}
F_{57}\! \left(x \right) = F_{51}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{55}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{20}\! \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_{64}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{48}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{40}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{79}\! \left(x \right)+F_{83}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{44}\! \left(x \right)
F_{82}\! \left(x \right) = F_{78}\! \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_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{25}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{106}\! \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_{96}\! \left(x \right)
F_{93}\! \left(x \right) = F_{86}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{96}\! \left(x \right) = F_{90}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{102}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{94}\! \left(x \right)
F_{101}\! \left(x \right) = F_{97}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \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) = 3 F_{20}\! \left(x \right)+F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{12}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{87}\! \left(x \right)
F_{110}\! \left(x \right) = F_{106}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{103}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{111}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)+F_{87}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{35}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{137}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{123}\! \left(x \right)+F_{20}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{12}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{120}\! \left(x \right)+F_{20}\! \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_{122}\! \left(x \right)+F_{26}\! \left(x \right)
F_{126}\! \left(x \right) = F_{119}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)+F_{133}\! \left(x \right)+F_{20}\! \left(x \right)
F_{128}\! \left(x \right) = 0
F_{129}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{122}\! \left(x \right)
F_{132}\! \left(x \right) = F_{127}\! \left(x \right)
F_{133}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{134}\! \left(x \right)+F_{26}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{141}\! \left(x \right)+F_{145}\! \left(x \right)+F_{20}\! \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_{48}\! \left(x \right)
F_{140}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{138}\! \left(x \right)+F_{88}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{143}\! \left(x \right) = F_{36}\! \left(x \right)
F_{144}\! \left(x \right) = F_{137}\! \left(x \right)
F_{145}\! \left(x \right) = F_{12}\! \left(x \right) F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{134}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{145}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{12}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{147}\! \left(x \right)+F_{36}\! \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_39(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_29(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) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_12(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_1(x) + F_26(x))
Eq(F_29(x), F_20(x) + F_30(x) + F_34(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_10(x))
Eq(F_33(x), F_29(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_26(x) + F_36(x))
Eq(F_36(x), F_20(x) + F_34(x) + F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_10(x) + F_36(x))
Eq(F_39(x), F_14(x) + F_40(x))
Eq(F_40(x), F_116(x) + F_20(x) + F_41(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_77(x))
Eq(F_43(x), F_44(x) + F_6(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_12(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_12(x)*F_47(x))
Eq(F_50(x), F_51(x) + F_67(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_57(x))
Eq(F_54(x), F_12(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), x**2)
Eq(F_57(x), F_51(x) + F_58(x))
Eq(F_58(x), 2*F_20(x) + F_59(x) + F_63(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_55(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_12(x) + F_64(x))
Eq(F_67(x), 2*F_20(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_64(x) + F_74(x))
Eq(F_74(x), 2*F_20(x) + F_72(x) + F_75(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_48(x) + F_74(x))
Eq(F_77(x), F_40(x) + F_78(x))
Eq(F_78(x), 2*F_20(x) + F_79(x) + F_83(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_44(x))
Eq(F_82(x), F_78(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) + F_87(x))
Eq(F_86(x), F_25(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_12(x)*F_85(x))
Eq(F_89(x), F_106(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_96(x))
Eq(F_93(x), F_86(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_12(x)*F_86(x))
Eq(F_96(x), F_90(x) + F_97(x))
Eq(F_97(x), F_102(x) + 3*F_20(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_94(x))
Eq(F_101(x), F_97(x))
Eq(F_102(x), F_103(x)*F_12(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) + F_111(x) + 3*F_20(x))
Eq(F_107(x), F_108(x)*F_12(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_87(x))
Eq(F_110(x), F_106(x))
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_103(x) + F_113(x))
Eq(F_113(x), F_111(x) + F_114(x) + 3*F_20(x))
Eq(F_114(x), F_115(x)*F_12(x))
Eq(F_115(x), F_113(x) + F_87(x))
Eq(F_116(x), F_117(x)*F_12(x))
Eq(F_117(x), F_118(x) + F_35(x))
Eq(F_118(x), F_119(x) + F_137(x))
Eq(F_119(x), F_120(x) + F_123(x) + F_20(x))
Eq(F_120(x), F_12(x)*F_121(x))
Eq(F_121(x), F_12(x) + F_122(x))
Eq(F_122(x), F_120(x) + F_20(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_122(x) + F_26(x))
Eq(F_126(x), F_119(x) + F_127(x))
Eq(F_127(x), F_128(x) + F_129(x) + F_133(x) + F_20(x))
Eq(F_128(x), 0)
Eq(F_129(x), F_12(x)*F_130(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_122(x))
Eq(F_132(x), F_127(x))
Eq(F_133(x), F_12(x)*F_134(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_12(x)*F_136(x))
Eq(F_136(x), F_134(x) + F_26(x))
Eq(F_137(x), F_138(x) + F_141(x) + F_145(x) + F_20(x))
Eq(F_138(x), F_12(x)*F_139(x))
Eq(F_139(x), F_140(x) + F_48(x))
Eq(F_140(x), F_138(x) + 2*F_20(x) + F_88(x))
Eq(F_141(x), F_12(x)*F_142(x))
Eq(F_142(x), F_143(x) + F_144(x))
Eq(F_143(x), F_36(x))
Eq(F_144(x), F_137(x))
Eq(F_145(x), F_12(x)*F_146(x))
Eq(F_146(x), F_134(x) + F_147(x))
Eq(F_147(x), F_145(x) + F_148(x) + 2*F_20(x))
Eq(F_148(x), F_12(x)*F_149(x))
Eq(F_149(x), F_147(x) + F_36(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": [1, 3, 2, 0], "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, 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": [1, 3, 2, 0], "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, 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": [1, 3, 2, 0], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [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": [1, 3, 2, 0], "pos": [[0, 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": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": 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