0132_0213_1230_2310
Counting sequence:
1, 1, 2, 6, 20, 62, 169, 412, 928, 1984, 4105, 8330, 16724, 33402, 66577, 132656, 264432, 527468, 1052865, 2102798, 4201588, 8397846, 16788761, 33568676, 67126240, 134238712, 268460569, 536900722, 1073776948, 2147524754, 4295015105, 8589989880, 17179932784, 34359811172, 68719559697, 137439047606, 274878013332, 549755933678, 1099511762185, 2199023405868, 4398046678688, 8796093208496, 17592186250921, 35184372317146, 70368744429460, 140737488632362, 281474977014769, 562949953754432, 1125899907206768, 2251799814082524, 4503599627803105, 9007199255211230, 18014398509992244, 36028797019516742, 72057594038525817, 144115188076501556, 288230376152408032, 576460752304173288, 1152921504607653305, 2305843009214559938, 4611686018428316788, 9223372036855770946, 18446744073710616481, 36893488147420241416, 73786976294839421680, 147573952589677709012, 295147905179354206769, 590295810358707121542, 1180591620717412866388, 2361183241434824267294, 4722366482869646976105, 9444732965739292296380, 18889465931478582835104, 37778931862957163806112, 75557863725914325636937, 151115727451828649182506, 302231454903657296152532, 604462909807314589966298, 1208925819614629177462225, 2417851639229258352317008, 4835703278458516701883888, 9671406556917033400869196, 19342813113834066798685441, 38685626227668133594157486, 77371252455336267184934900, 154742504910672534366316662, 309485009821345068728900569, 618970019642690137453882052, 1237940039285380274903651808, 2475880078570760549802991064, 4951760157141521099601462105, 9903520314283042199198189330, 19807040628566084398391421364, 39614081257132168796777655282, 79228162514264337593549885057, 158456325028528675187094098456, 316912650057057350374182270832, 633825300114114700748358352708, 1267650600228229401496710244945, 2535301200456458802993413749078, 5070602400912917605986820467988
Generating function in Maple syntax:
(2*x^8-x^7-4*x^6-4*x^5+13*x^4-18*x^3+15*x^2-6*x+1)/(2*x-1)/(x-1)^5
Generating function in latex syntax:
\frac{2 x^{8}-x^{7}-4 x^{6}-4 x^{5}+13 x^{4}-18 x^{3}+15 x^{2}-6 x +1}{\left(2 x -1\right) \left(x -1\right)^{5}}
Generating function in sympy syntax:
(2*x**8 - x**7 - 4*x**6 - 4*x**5 + 13*x**4 - 18*x**3 + 15*x**2 - 6*x + 1)/((x - 1)**5*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x-1)^5*F(x)+2*x^8-x^7-4*x^6-4*x^5+13*x^4-18*x^3+15*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x -1\right)^{5} F \! \left(x \right)+2 x^{8}-x^{7}-4 x^{6}-4 x^{5}+13 x^{4}-18 x^{3}+15 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,-16-2/3*n^3-25/12*n^2+20/3*n+1/12*n^4+4*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ -16-\frac{2 n^{3}}{3}-\frac{25 n^{2}}{12}+\frac{20 n}{3}+\frac{n^{4}}{12}+4 \,2^{n} & \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) = 62
a(6) = 169
a(7) = 412
a(8) = 928
a(n+1) = -1/12*n^4+n^3+7/12*n^2+2*a(n)-25/2*n+20, 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) = 20
a \! \left(5\right) = 62
a \! \left(6\right) = 169
a \! \left(7\right) = 412
a \! \left(8\right) = 928
a \! \left(n +1\right) = -\frac{n^{4}}{12}+n^{3}+\frac{7 n^{2}}{12}+2 a \! \left(n \right)-\frac{25 n}{2}+20, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15280/
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[26,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[19,x]+F[22,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[1,x]+F[19,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[19,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[13,x]
F[26,x] = F[27,x]+F[38,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[21,x]+F[30,x]
F[30,x] = F[19,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]+F[35,x]
F[32,x] = 0
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[19,x]+F[31,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[19,x]+F[37,x]
F[37,x] = F[35,x]
F[38,x] = F[124,x]+F[32,x]+F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]+F[61,x]
F[41,x] = F[42,x]+F[6,x]
F[42,x] = F[32,x]+F[43,x]+F[48,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[10,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[19,x]+F[45,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[47,x]+F[50,x]
F[50,x] = F[51,x]+F[59,x]
F[51,x] = F[32,x]+F[52,x]+F[54,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[12,x]+F[22,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[18,x]+F[56,x]
F[56,x] = F[37,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[12,x]*F[37,x]
F[59,x] = F[60,x]
F[60,x] = F[12,x]*F[50,x]
F[61,x] = F[62,x]+F[89,x]
F[62,x] = F[32,x]+F[63,x]+F[65,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[6,x]+F[62,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[67,x]+F[72,x]
F[67,x] = F[19,x]+F[68,x]
F[68,x] = F[32,x]+F[69,x]+F[71,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[10,x]+F[68,x]
F[71,x] = F[12,x]*F[67,x]
F[72,x] = F[73,x]+F[82,x]
F[73,x] = F[32,x]+F[33,x]+F[74,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[76,x]+F[80,x]
F[76,x] = F[19,x]+F[77,x]
F[77,x] = F[23,x]+F[32,x]+F[78,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[12,x]+F[77,x]
F[80,x] = F[37,x]+F[81,x]
F[81,x] = F[58,x]
F[82,x] = 2*F[32,x]+F[83,x]+F[88,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[45,x]+F[85,x]
F[85,x] = 2*F[32,x]+F[83,x]+F[86,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[31,x]+F[85,x]
F[88,x] = F[12,x]*F[72,x]
F[89,x] = F[32,x]+F[90,x]+F[92,x]+F[97,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[42,x]+F[89,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[68,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[12,x]*F[96,x]
F[96,x] = F[37,x]+F[94,x]
F[97,x] = F[12,x]*F[98,x]
F[98,x] = F[87,x]+F[99,x]
F[99,x] = F[100,x]+F[114,x]
F[100,x] = F[101,x]+F[107,x]+F[109,x]+F[32,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[103,x]+F[37,x]
F[103,x] = 2*F[32,x]+F[101,x]+F[104,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[106,x]+F[37,x]
F[106,x] = F[104,x]
F[107,x] = F[108,x]*F[12,x]
F[108,x] = F[77,x]+F[81,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[111,x]+F[80,x]
F[111,x] = F[106,x]+F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[106,x]*F[12,x]
F[114,x] = 3*F[32,x]+F[115,x]+F[123,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[120,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]*F[12,x]
F[119,x] = F[117,x]+F[37,x]
F[120,x] = 3*F[32,x]+F[115,x]+F[121,x]
F[121,x] = F[12,x]*F[122,x]
F[122,x] = F[103,x]+F[120,x]
F[123,x] = F[12,x]*F[99,x]
F[124,x] = F[12,x]*F[125,x]
F[125,x] = F[126,x]+F[137,x]
F[126,x] = F[127,x]+F[27,x]
F[127,x] = F[128,x]+F[136,x]+F[32,x]
F[128,x] = F[12,x]*F[129,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[10,x]+F[131,x]
F[131,x] = F[32,x]+F[43,x]+F[46,x]
F[132,x] = F[133,x]+F[68,x]
F[133,x] = F[134,x]+F[32,x]+F[86,x]+F[92,x]
F[134,x] = F[12,x]*F[135,x]
F[135,x] = F[131,x]+F[133,x]
F[136,x] = F[12,x]*F[126,x]
F[137,x] = F[138,x]+F[143,x]
F[138,x] = F[139,x]+F[32,x]+F[74,x]
F[139,x] = F[12,x]*F[140,x]
F[140,x] = F[141,x]+F[142,x]
F[141,x] = F[19,x]+F[37,x]
F[142,x] = F[103,x]+F[31,x]
F[143,x] = 2*F[32,x]+F[144,x]+F[152,x]
F[144,x] = F[12,x]*F[145,x]
F[145,x] = F[146,x]+F[148,x]
F[146,x] = F[147,x]+F[45,x]
F[147,x] = F[118,x]
F[148,x] = F[149,x]+F[85,x]
F[149,x] = 3*F[32,x]+F[121,x]+F[150,x]
F[150,x] = F[12,x]*F[151,x]
F[151,x] = F[147,x]+F[149,x]
F[152,x] = F[12,x]*F[137,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_{26}\! \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_{19}\! \left(x \right)+F_{22}\! \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_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{38}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{21}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = 0
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{19}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{124}\! \left(x \right)+F_{32}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{61}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{6}\! \left(x \right)
F_{42}\! \left(x \right) = F_{32}\! \left(x \right)+F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{59}\! \left(x \right)
F_{51}\! \left(x \right) = F_{32}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right)+F_{22}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{18}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{37}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{89}\! \left(x \right)
F_{62}\! \left(x \right) = F_{32}\! \left(x \right)+F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{6}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{67}\! \left(x \right) = F_{19}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{32}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{10}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{82}\! \left(x \right)
F_{73}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{19}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{23}\! \left(x \right)+F_{32}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{37}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{58}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{83}\! \left(x \right)+F_{88}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{45}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{31}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{89}\! \left(x \right) = F_{32}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)+F_{97}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{42}\! \left(x \right)+F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{68}\! \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_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{37}\! \left(x \right)+F_{94}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{87}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{114}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{107}\! \left(x \right)+F_{109}\! \left(x \right)+F_{32}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{37}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{101}\! \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_{106}\! \left(x \right)+F_{37}\! \left(x \right)
F_{106}\! \left(x \right) = F_{104}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{12}\! \left(x \right)
F_{108}\! \left(x \right) = F_{77}\! \left(x \right)+F_{81}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{80}\! \left(x \right)
F_{111}\! \left(x \right) = F_{106}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = 3 F_{32}\! \left(x \right)+F_{115}\! \left(x \right)+F_{123}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{120}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{117}\! \left(x \right)+F_{37}\! \left(x \right)
F_{120}\! \left(x \right) = 3 F_{32}\! \left(x \right)+F_{115}\! \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_{103}\! \left(x \right)+F_{120}\! \left(x \right)
F_{123}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{124}\! \left(x \right) = F_{12}\! \left(x \right) F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{137}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{27}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{136}\! \left(x \right)+F_{32}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{10}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{32}\! \left(x \right)+F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{68}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{32}\! \left(x \right)+F_{86}\! \left(x \right)+F_{92}\! \left(x \right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right) F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{131}\! \left(x \right)+F_{133}\! \left(x \right)
F_{136}\! \left(x \right) = F_{12}\! \left(x \right) F_{126}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{143}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{32}\! \left(x \right)+F_{74}\! \left(x \right)
F_{139}\! \left(x \right) = F_{12}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{142}\! \left(x \right)
F_{141}\! \left(x \right) = F_{19}\! \left(x \right)+F_{37}\! \left(x \right)
F_{142}\! \left(x \right) = F_{103}\! \left(x \right)+F_{31}\! \left(x \right)
F_{143}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{144}\! \left(x \right)+F_{152}\! \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_{148}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{45}\! \left(x \right)
F_{147}\! \left(x \right) = F_{118}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{85}\! \left(x \right)
F_{149}\! \left(x \right) = 3 F_{32}\! \left(x \right)+F_{121}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{12}\! \left(x \right) F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{147}\! \left(x \right)+F_{149}\! \left(x \right)
F_{152}\! \left(x \right) = F_{12}\! \left(x \right) F_{137}\! \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_26(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_19(x) + F_22(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_1(x) + F_19(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_13(x))
Eq(F_26(x), F_27(x) + F_38(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_21(x) + F_30(x))
Eq(F_30(x), F_19(x) + F_31(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_35(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_19(x) + F_31(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_19(x) + F_37(x))
Eq(F_37(x), F_35(x))
Eq(F_38(x), F_124(x) + F_32(x) + F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_61(x))
Eq(F_41(x), F_42(x) + F_6(x))
Eq(F_42(x), F_32(x) + F_43(x) + F_48(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_10(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_19(x) + F_45(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_47(x) + F_50(x))
Eq(F_50(x), F_51(x) + F_59(x))
Eq(F_51(x), F_32(x) + F_52(x) + F_54(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_12(x) + F_22(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_18(x) + F_56(x))
Eq(F_56(x), F_37(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_12(x)*F_37(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_12(x)*F_50(x))
Eq(F_61(x), F_62(x) + F_89(x))
Eq(F_62(x), F_32(x) + F_63(x) + F_65(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_6(x) + F_62(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_72(x))
Eq(F_67(x), F_19(x) + F_68(x))
Eq(F_68(x), F_32(x) + F_69(x) + F_71(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_10(x) + F_68(x))
Eq(F_71(x), F_12(x)*F_67(x))
Eq(F_72(x), F_73(x) + F_82(x))
Eq(F_73(x), F_32(x) + F_33(x) + F_74(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_80(x))
Eq(F_76(x), F_19(x) + F_77(x))
Eq(F_77(x), F_23(x) + F_32(x) + F_78(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_12(x) + F_77(x))
Eq(F_80(x), F_37(x) + F_81(x))
Eq(F_81(x), F_58(x))
Eq(F_82(x), 2*F_32(x) + F_83(x) + F_88(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_45(x) + F_85(x))
Eq(F_85(x), 2*F_32(x) + F_83(x) + F_86(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_31(x) + F_85(x))
Eq(F_88(x), F_12(x)*F_72(x))
Eq(F_89(x), F_32(x) + F_90(x) + F_92(x) + F_97(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_42(x) + F_89(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_68(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_12(x)*F_96(x))
Eq(F_96(x), F_37(x) + F_94(x))
Eq(F_97(x), F_12(x)*F_98(x))
Eq(F_98(x), F_87(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_114(x))
Eq(F_100(x), F_101(x) + F_107(x) + F_109(x) + F_32(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_103(x) + F_37(x))
Eq(F_103(x), F_101(x) + F_104(x) + 2*F_32(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_106(x) + F_37(x))
Eq(F_106(x), F_104(x))
Eq(F_107(x), F_108(x)*F_12(x))
Eq(F_108(x), F_77(x) + F_81(x))
Eq(F_109(x), F_110(x)*F_12(x))
Eq(F_110(x), F_111(x) + F_80(x))
Eq(F_111(x), F_106(x) + F_112(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_106(x)*F_12(x))
Eq(F_114(x), F_115(x) + F_123(x) + 3*F_32(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_120(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)*F_12(x))
Eq(F_119(x), F_117(x) + F_37(x))
Eq(F_120(x), F_115(x) + F_121(x) + 3*F_32(x))
Eq(F_121(x), F_12(x)*F_122(x))
Eq(F_122(x), F_103(x) + F_120(x))
Eq(F_123(x), F_12(x)*F_99(x))
Eq(F_124(x), F_12(x)*F_125(x))
Eq(F_125(x), F_126(x) + F_137(x))
Eq(F_126(x), F_127(x) + F_27(x))
Eq(F_127(x), F_128(x) + F_136(x) + F_32(x))
Eq(F_128(x), F_12(x)*F_129(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_10(x) + F_131(x))
Eq(F_131(x), F_32(x) + F_43(x) + F_46(x))
Eq(F_132(x), F_133(x) + F_68(x))
Eq(F_133(x), F_134(x) + F_32(x) + F_86(x) + F_92(x))
Eq(F_134(x), F_12(x)*F_135(x))
Eq(F_135(x), F_131(x) + F_133(x))
Eq(F_136(x), F_12(x)*F_126(x))
Eq(F_137(x), F_138(x) + F_143(x))
Eq(F_138(x), F_139(x) + F_32(x) + F_74(x))
Eq(F_139(x), F_12(x)*F_140(x))
Eq(F_140(x), F_141(x) + F_142(x))
Eq(F_141(x), F_19(x) + F_37(x))
Eq(F_142(x), F_103(x) + F_31(x))
Eq(F_143(x), F_144(x) + F_152(x) + 2*F_32(x))
Eq(F_144(x), F_12(x)*F_145(x))
Eq(F_145(x), F_146(x) + F_148(x))
Eq(F_146(x), F_147(x) + F_45(x))
Eq(F_147(x), F_118(x))
Eq(F_148(x), F_149(x) + F_85(x))
Eq(F_149(x), F_121(x) + F_150(x) + 3*F_32(x))
Eq(F_150(x), F_12(x)*F_151(x))
Eq(F_151(x), F_147(x) + F_149(x))
Eq(F_152(x), F_12(x)*F_137(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": [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, 1, 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": [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, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": 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