0132_2130_3102
Counting sequence:
1, 1, 2, 6, 21, 71, 219, 626, 1698, 4452, 11428, 28966, 72907, 182915, 458590, 1150877, 2894324, 7299391, 18468191, 46885660, 119437550, 305268086, 782671392, 2012470416, 5188157511, 13406252581, 34712884554, 90042441271, 233921270608, 608500149057, 1584650190763, 4130585814726, 10775297657242, 28127392992520, 73462194615980, 191951563829882, 501739661852339, 1311884442266151, 3430988792226566, 8974905771451665, 23480706181297500, 61439793701234531, 160781019281436807, 420782180425080176, 1101311534807801526, 2882620260370495866, 7545435441024765064, 19751357297076186916, 51703772210762532943, 135349808643863803337, 354324490321017465298, 927579576300961308011, 2428322477739458808152, 6357197016883205316325, 16642871974667971852595, 43570595311338854889562, 114067204843290005741954, 298627474885624421786636, 781807874442591018371316, 2046780935282607375825870, 5358503442236636534634075, 14028664251362291941259851, 36727354636206982401872622, 96153121370830480786710661, 251731434744914413445085316, 659039996507684519103052551, 1725386107125784863527989999, 4517113277379322902704906436, 11825943321048526272399670078, 30960695250649642263995180542, 81056098287841832132628911408, 212207508744214547040640352696, 555566240968603877869277028887, 1454490829583876637870458708205, 3807905457081788060255878694810, 9969223916577121625380518283167, 26099762953936473427046510144544, 68330058088356165529034161939721, 178890397233757537725643593725691, 468341104721478305451407201927150, 1226132857655533285648791289828650, 3210057346672518816498820286257296, 8404038933096630732056316609305212, 22002058941695098865037474581555746, 57602136845058906076787241839912131, 150804349448847215368972095009526511, 394810907109455237370181251481235734, 1033628362887528250447959857969753081, 2706074163148442836160583766701313388, 7084594088897343125398863391687509547, 18547708026501161907634918362686152343, 48558529833039586972213583581866917656, 127127881150443703784985615840417650822, 332825112959707423482920957693052081410, 871347456382728258950747553354665919000, 2281217253438393556096849421682541354572, 5972304298314680511062745024200732563359, 15635695630032419692994481263154573179281, 40934782568355801264484162443071960316066, 107168652027210884502785195286158340908755, 280571173415667756026297759500156915762600
Generating function in Maple syntax:
(5*x^10-22*x^9+12*x^8+89*x^7-249*x^6+354*x^5-316*x^4+179*x^3-62*x^2+12*x-1)/(x^2-3*x+1)/(2*x-1)^3/(x-1)^4
Generating function in latex syntax:
\frac{5 x^{10}-22 x^{9}+12 x^{8}+89 x^{7}-249 x^{6}+354 x^{5}-316 x^{4}+179 x^{3}-62 x^{2}+12 x -1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{4}}
Generating function in sympy syntax:
(5*x**10 - 22*x**9 + 12*x**8 + 89*x**7 - 249*x**6 + 354*x**5 - 316*x**4 + 179*x**3 - 62*x**2 + 12*x - 1)/((x - 1)**4*(2*x - 1)**3*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(2*x-1)^3*(x-1)^4*F(x)+5*x^10-22*x^9+12*x^8+89*x^7-249*x^6+354*x^5-316*x^4+179*x^3-62*x^2+12*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{4} F \! \left(x \right)+5 x^{10}-22 x^{9}+12 x^{8}+89 x^{7}-249 x^{6}+354 x^{5}-316 x^{4}+179 x^{3}-62 x^{2}+12 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/5*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)-1/5*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)+1/480*(15*n^2+105*n-270)*2^n-1/6*n^3-1/2*n^2+5/3*n-1)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}-\frac{\left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}+\frac{\left(15 n^{2}+105 n -270\right) 2^{n}}{480}-\frac{n^{3}}{6}-\frac{n^{2}}{2}+\\\frac{5 n}{3}-1 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 71
a(6) = 219
a(7) = 626
a(8) = 1698
a(9) = 4452
a(10) = 11428
a(n+5) = 8*a(n)-36*a(n+1)+50*a(n+2)-31*a(n+3)+9*a(n+4)-1/6*(-1+n)*(n^2-2*n-36), n >= 11
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) = 71
a \! \left(6\right) = 219
a \! \left(7\right) = 626
a \! \left(8\right) = 1698
a \! \left(9\right) = 4452
a \! \left(10\right) = 11428
a \! \left(n +5\right) = 8 a \! \left(n \right)-36 a \! \left(n +1\right)+50 a \! \left(n +2\right)-31 a \! \left(n +3\right)+9 a \! \left(n +4\right)-\frac{\left(-1+n \right) \left(n^{2}-2 n -36\right)}{6}, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14742/
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[32,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[20,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[21,x]+F[22,x]+F[31,x]
F[21,x] = 0
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]+F[27,x]
F[24,x] = F[11,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[24,x]*F[4,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[22,x]
F[29,x] = F[30,x]
F[30,x] = F[27,x]*F[4,x]
F[31,x] = F[13,x]*F[4,x]
F[32,x] = F[33,x]+F[47,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[1,x]+F[14,x]
F[37,x] = F[33,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[33,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[41,x]
F[44,x] = F[38,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[44,x]
F[47,x] = F[21,x]+F[48,x]+F[99,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[76,x]
F[50,x] = F[51,x]+F[7,x]
F[51,x] = F[21,x]+F[22,x]+F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[13,x]+F[54,x]
F[54,x] = F[55,x]+F[63,x]
F[55,x] = F[21,x]+F[56,x]+F[58,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[24,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[17,x]+F[60,x]
F[60,x] = F[55,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[60,x]
F[63,x] = F[21,x]+F[64,x]+F[69,x]+F[75,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[25,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[66,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[27,x]+F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = 2*F[21,x]+F[64,x]+F[69,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[71,x]
F[75,x] = F[4,x]*F[54,x]
F[76,x] = F[77,x]+F[98,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[82,x]
F[80,x] = F[7,x]+F[81,x]
F[81,x] = F[22,x]
F[82,x] = F[77,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[95,x]
F[86,x] = F[87,x]+F[93,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[11,x]+F[28,x]
F[91,x] = F[87,x]+F[92,x]
F[92,x] = F[84,x]
F[93,x] = F[94,x]
F[94,x] = F[4,x]*F[86,x]
F[95,x] = F[92,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[95,x]
F[98,x] = F[84,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[109,x]
F[101,x] = F[102,x]+F[33,x]
F[102,x] = F[103,x]+F[108,x]+F[21,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[11,x]+F[20,x]
F[106,x] = F[107,x]+F[87,x]
F[107,x] = F[84,x]
F[108,x] = F[101,x]*F[4,x]
F[109,x] = F[110,x]+F[119,x]
F[110,x] = F[111,x]+F[114,x]+F[21,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]
F[113,x] = F[14,x]+F[55,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[41,x]
F[116,x] = F[110,x]+F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[116,x]*F[4,x]
F[119,x] = F[120,x]+F[123,x]+F[132,x]+F[21,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]
F[122,x] = F[20,x]+F[63,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[125,x]+F[86,x]
F[125,x] = F[126,x]+F[130,x]
F[126,x] = 2*F[21,x]+F[123,x]+F[127,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]
F[129,x] = F[28,x]+F[72,x]
F[130,x] = F[131,x]
F[131,x] = F[125,x]*F[4,x]
F[132,x] = F[109,x]*F[4,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_{32}\! \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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{20}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{31}\! \left(x \right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{22}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{47}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{33}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{21}\! \left(x \right)+F_{48}\! \left(x \right)+F_{99}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{76}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{7}\! \left(x \right)
F_{51}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{63}\! \left(x \right)
F_{55}\! \left(x \right) = F_{21}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{24}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{17}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{55}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{21}\! \left(x \right)+F_{64}\! \left(x \right)+F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{25}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{27}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{64}\! \left(x \right)+F_{69}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{98}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \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_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{7}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{22}\! \left(x \right)
F_{82}\! \left(x \right) = F_{77}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{95}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{93}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \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_{11}\! \left(x \right)+F_{28}\! \left(x \right)
F_{91}\! \left(x \right) = F_{87}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{84}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{95}\! \left(x \right) = F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{84}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{109}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{33}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{108}\! \left(x \right)+F_{21}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{11}\! \left(x \right)+F_{20}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{87}\! \left(x \right)
F_{107}\! \left(x \right) = F_{84}\! \left(x \right)
F_{108}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{119}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{114}\! \left(x \right)+F_{21}\! \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_{113}\! \left(x \right) = F_{14}\! \left(x \right)+F_{55}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{41}\! \left(x \right)
F_{116}\! \left(x \right) = F_{110}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{123}\! \left(x \right)+F_{132}\! \left(x \right)+F_{21}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{20}\! \left(x \right)+F_{63}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{86}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{130}\! \left(x \right)
F_{126}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{123}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{28}\! \left(x \right)+F_{72}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \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_32(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_20(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_22(x) + F_31(x))
Eq(F_21(x), 0)
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_24(x) + F_27(x))
Eq(F_24(x), F_11(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_24(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_22(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_27(x)*F_4(x))
Eq(F_31(x), F_13(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_47(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_1(x) + F_14(x))
Eq(F_37(x), F_33(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_33(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_41(x))
Eq(F_44(x), F_38(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_44(x))
Eq(F_47(x), F_21(x) + F_48(x) + F_99(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_76(x))
Eq(F_50(x), F_51(x) + F_7(x))
Eq(F_51(x), F_21(x) + F_22(x) + F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_13(x) + F_54(x))
Eq(F_54(x), F_55(x) + F_63(x))
Eq(F_55(x), F_21(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_24(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_17(x) + F_60(x))
Eq(F_60(x), F_55(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_60(x))
Eq(F_63(x), F_21(x) + F_64(x) + F_69(x) + F_75(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_25(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_66(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_27(x) + F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), 2*F_21(x) + F_64(x) + F_69(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_71(x))
Eq(F_75(x), F_4(x)*F_54(x))
Eq(F_76(x), F_77(x) + F_98(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_82(x))
Eq(F_80(x), F_7(x) + F_81(x))
Eq(F_81(x), F_22(x))
Eq(F_82(x), F_77(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_95(x))
Eq(F_86(x), F_87(x) + F_93(x))
Eq(F_87(x), F_88(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_11(x) + F_28(x))
Eq(F_91(x), F_87(x) + F_92(x))
Eq(F_92(x), F_84(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_4(x)*F_86(x))
Eq(F_95(x), F_92(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_95(x))
Eq(F_98(x), F_84(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_109(x))
Eq(F_101(x), F_102(x) + F_33(x))
Eq(F_102(x), F_103(x) + F_108(x) + F_21(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_11(x) + F_20(x))
Eq(F_106(x), F_107(x) + F_87(x))
Eq(F_107(x), F_84(x))
Eq(F_108(x), F_101(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_119(x))
Eq(F_110(x), F_111(x) + F_114(x) + F_21(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_14(x) + F_55(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x) + F_41(x))
Eq(F_116(x), F_110(x) + F_117(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_116(x)*F_4(x))
Eq(F_119(x), F_120(x) + F_123(x) + F_132(x) + F_21(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_20(x) + F_63(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x) + F_86(x))
Eq(F_125(x), F_126(x) + F_130(x))
Eq(F_126(x), F_123(x) + F_127(x) + 2*F_21(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_28(x) + F_72(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_125(x)*F_4(x))
Eq(F_132(x), F_109(x)*F_4(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": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"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, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "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, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"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, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "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", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"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, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], 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