0132_1230_2301
Counting sequence:
1, 1, 2, 6, 21, 74, 249, 792, 2394, 6941, 19479, 53323, 143275, 379721, 996456, 2596798, 6735913, 17421708, 44987569, 116098066, 299635282, 773762271, 1999891807, 5174530901, 13404160931, 34763222379, 90260551984, 234609144152, 610412760209, 1589616256126, 4142933856089, 10805094004268, 28197723094490, 73625403386881, 192325225999511, 502585770425823, 1313782817828523, 3435215040064813, 8984251620308264, 23501253304863666, 61484736239043657, 160878875816334416, 420994386169268337, 1101770031156613446, 2883607621812270066, 7547555299443150659, 19755896081075681919, 51713465505273044137, 135370461870279988099, 354368400417384370511, 927672744518252580624, 2428519791698133026188, 6357614162798690559505, 16643752428395122838466, 43572450794385331590841, 114071109464166936022048, 298635680444145490893658, 781825096207566083214693, 2046817036137220377791959, 5358579030652782321112691, 14028822345723611155228907, 36727684948218052263612561, 96153810817890235681287592, 251732872438030658183353766, 659042991797753487691589801, 1725392342125281777356534164, 4517126245440406720519794929, 11825970271741617962054688122, 30960751218071161898774895314, 81056214428542520207966002471, 212207749584905173392546372959, 555566740063711536154905678333, 1454491863191840575964054988195, 3807907596313804800205160636851, 9969228341434516074238083659696, 26099772101160350745549289222848, 68330076987266829973354307306193, 178890436259394152160391639870598, 468341185266161037276075966893529, 1226133023807275618934388488682516, 3210057689251872949794362668800282, 8404039639109309386999754637899081, 22002060396032859861436371753279447, 57602139839568161262223707587311111, 150804355611951043764351627661820011, 394810919788669233488412035799825269, 1033628388961640327896281898032780264, 2706074216747377974594782856474563482, 7084594199035320995570039724119206729, 18547708252734704087038163600501351256, 48558530297576586714052531737763537969, 127127882103967019044549772581468348078, 332825114916271655573464482171118189810, 871347460396129866313950404577626934411, 2281217261668218937266057489211919485951, 5972304315185327366443907410525997787473, 15635695664605609110156581580537314816003, 40934782639185778552236480251700252234903, 107168652172277650066403197419937314302224, 280571173712694137292274761138353185910516, 734544868628609702149712065196999190632657
Generating function in Maple syntax:
(2*x^9-20*x^8+94*x^7-240*x^6+351*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{2 x^{9}-20 x^{8}+94 x^{7}-240 x^{6}+351 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:
(2*x**9 - 20*x**8 + 94*x**7 - 240*x**6 + 351*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)-2*x^9+20*x^8-94*x^7+240*x^6-351*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)-2 x^{9}+20 x^{8}-94 x^{7}+240 x^{6}-351 x^{5}+316 x^{4}-179 x^{3}+62 x^{2}-12 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/120*(36*5^(1/2)+60)*(3/2-1/2*5^(1/2))^(-n)+1/120*(-36*5^(1/2)+60)*(3/2+1/2*5^(1/2))^(-n)+1/6*(n+2)*((3/4*n-27/4)*2^n+n^2+n+6))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(36 \sqrt{5}+60\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{120}+\frac{\left(-36 \sqrt{5}+60\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{120}+\\\frac{\left(n +2\right) \left(\left(\frac{3 n}{4}-\frac{27}{4}\right) 2^{n}+n^{2}+n +6\right)}{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) = 21
a(5) = 74
a(6) = 249
a(7) = 792
a(8) = 2394
a(9) = 6941
a(n+5) = 8*a(n)-36*a(n+1)+50*a(n+2)-31*a(n+3)+9*a(n+4)+1/6*(n+3)*(n^2-6*n+2), n >= 10
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) = 74
a \! \left(6\right) = 249
a \! \left(7\right) = 792
a \! \left(8\right) = 2394
a \! \left(9\right) = 6941
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(n +3\right) \left(n^{2}-6 n +2\right)}{6}, \quad n \geq 10
Specification 1
Strategy pack name: insertion_point_col_placements_req_corrob
Tree: http://permpal.com/tree/293/
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[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[85,x]+F[9,x]
F[9,x] = F[10,x]*F[14,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[13,x]
F[12,x] = x
F[13,x] = F[1,x]+F[10,x]
F[14,x] = F[15,x]+F[53,x]
F[15,x] = F[1,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[12,x]*F[18,x]
F[18,x] = F[19,x]+F[22,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[19,x]
F[22,x] = F[23,x]+F[35,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[1,x]+F[12,x]
F[27,x] = F[23,x]+F[28,x]
F[28,x] = F[29,x]+F[30,x]+F[34,x]
F[29,x] = 0
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[12,x]
F[33,x] = F[28,x]
F[34,x] = F[10,x]*F[12,x]
F[35,x] = F[29,x]+F[36,x]+F[51,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[20,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[20,x]
F[41,x] = F[35,x]+F[42,x]
F[42,x] = 2*F[29,x]+F[43,x]+F[47,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[39,x]
F[46,x] = F[42,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[29,x]+F[49,x]+F[51,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[20,x]+F[48,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[10,x]+F[48,x]
F[53,x] = F[10,x]+F[54,x]
F[54,x] = F[29,x]+F[55,x]+F[57,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[16,x]+F[54,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[59,x]+F[63,x]
F[59,x] = F[10,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[20,x]+F[60,x]
F[63,x] = F[54,x]+F[64,x]
F[64,x] = 2*F[29,x]+F[65,x]+F[84,x]
F[65,x] = F[66,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[12,x]+F[68,x]
F[71,x] = 2*F[29,x]+F[72,x]+F[80,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[71,x]+F[74,x]
F[74,x] = F[29,x]+F[75,x]+F[79,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[12,x]
F[78,x] = F[74,x]
F[79,x] = F[10,x]*F[12,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[68,x]
F[83,x] = F[71,x]
F[84,x] = F[12,x]*F[63,x]
F[85,x] = F[118,x]+F[86,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = F[10,x]*F[19,x]
F[88,x] = F[107,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[86,x]+F[92,x]
F[92,x] = F[10,x]*F[93,x]
F[93,x] = F[14,x]+F[94,x]
F[94,x] = F[87,x]+F[95,x]
F[95,x] = F[101,x]+F[96,x]
F[96,x] = F[29,x]+F[97,x]+F[99,x]
F[97,x] = F[12,x]*F[98,x]
F[98,x] = F[10,x]+F[96,x]
F[99,x] = F[100,x]*F[12,x]
F[100,x] = F[10,x]+F[96,x]
F[101,x] = F[102,x]+F[106,x]+F[29,x]
F[102,x] = F[10,x]*F[103,x]*F[12,x]
F[103,x] = F[104,x]+F[12,x]
F[104,x] = F[105,x]+F[29,x]+F[79,x]
F[105,x] = F[103,x]*F[12,x]
F[106,x] = F[12,x]*F[95,x]
F[107,x] = F[108,x]+F[117,x]+F[29,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[110,x]+F[112,x]
F[110,x] = F[10,x]*F[111,x]
F[111,x] = F[12,x]+F[74,x]
F[112,x] = F[113,x]+F[115,x]
F[113,x] = F[114,x]
F[114,x] = F[10,x]^2*F[12,x]
F[115,x] = F[116,x]
F[116,x] = F[12,x]*F[13,x]*F[71,x]
F[117,x] = F[12,x]*F[88,x]
F[118,x] = F[119,x]+F[127,x]
F[119,x] = F[120,x]+F[125,x]
F[120,x] = F[121,x]+F[123,x]+F[29,x]
F[121,x] = F[12,x]*F[122,x]
F[122,x] = F[10,x]+F[120,x]
F[123,x] = F[12,x]*F[124,x]
F[124,x] = F[10,x]+F[120,x]
F[125,x] = F[126,x]
F[126,x] = F[10,x]^2*F[20,x]
F[127,x] = F[128,x]+F[132,x]
F[128,x] = F[129,x]+F[130,x]+F[29,x]
F[129,x] = F[10,x]*F[12,x]*F[122,x]
F[130,x] = F[12,x]*F[131,x]
F[131,x] = F[128,x]+F[96,x]
F[132,x] = F[133,x]
F[133,x] = F[10,x]*F[101,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_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \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_{85}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{53}\! \left(x \right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{35}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{29}\! \left(x \right) = 0
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_{12}\! \left(x \right)
F_{33}\! \left(x \right) = F_{28}\! \left(x \right)
F_{34}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)+F_{36}\! \left(x \right)+F_{51}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \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_{20}\! \left(x \right)
F_{41}\! \left(x \right) = F_{35}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{39}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{29}\! \left(x \right)+F_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{20}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{10}\! \left(x \right)+F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{10}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{29}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{10}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{20}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{54}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{65}\! \left(x \right)+F_{84}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{72}\! \left(x \right)+F_{80}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{29}\! \left(x \right)+F_{75}\! \left(x \right)+F_{79}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{68}\! \left(x \right)
F_{83}\! \left(x \right) = F_{71}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{85}\! \left(x \right) = F_{118}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{10}\! \left(x \right) F_{19}\! \left(x \right)
F_{88}\! \left(x \right) = F_{107}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{86}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{10}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{14}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{87}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{29}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{10}\! \left(x \right)+F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \left(x \right)
F_{100}\! \left(x \right) = F_{10}\! \left(x \right)+F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{106}\! \left(x \right)+F_{29}\! \left(x \right)
F_{102}\! \left(x \right) = F_{10}\! \left(x \right) F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{29}\! \left(x \right)+F_{79}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{117}\! \left(x \right)+F_{29}\! \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_{112}\! \left(x \right)
F_{110}\! \left(x \right) = F_{10}\! \left(x \right) F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{12}\! \left(x \right)+F_{74}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{115}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{10} \left(x \right)^{2} F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right) F_{71}\! \left(x \right)
F_{117}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{127}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{125}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{123}\! \left(x \right)+F_{29}\! \left(x \right)
F_{121}\! \left(x \right) = F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{10}\! \left(x \right)+F_{120}\! \left(x \right)
F_{123}\! \left(x \right) = F_{12}\! \left(x \right) F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{10}\! \left(x \right)+F_{120}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{10} \left(x \right)^{2} F_{20}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{132}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{130}\! \left(x \right)+F_{29}\! \left(x \right)
F_{129}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{130}\! \left(x \right) = F_{12}\! \left(x \right) F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{128}\! \left(x \right)+F_{96}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{10}\! \left(x \right) F_{101}\! \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_0(x) + F_5(x))
Eq(F_5(x), F_2(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_85(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_14(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_13(x))
Eq(F_12(x), x)
Eq(F_13(x), F_1(x) + F_10(x))
Eq(F_14(x), F_15(x) + F_53(x))
Eq(F_15(x), F_1(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_12(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_22(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_19(x))
Eq(F_22(x), F_23(x) + F_35(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_1(x) + F_12(x))
Eq(F_27(x), F_23(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_30(x) + F_34(x))
Eq(F_29(x), 0)
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_12(x))
Eq(F_33(x), F_28(x))
Eq(F_34(x), F_10(x)*F_12(x))
Eq(F_35(x), F_29(x) + F_36(x) + F_51(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_20(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_20(x))
Eq(F_41(x), F_35(x) + F_42(x))
Eq(F_42(x), 2*F_29(x) + F_43(x) + F_47(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_39(x))
Eq(F_46(x), F_42(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_29(x) + F_49(x) + F_51(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_20(x) + F_48(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_10(x) + F_48(x))
Eq(F_53(x), F_10(x) + F_54(x))
Eq(F_54(x), F_29(x) + F_55(x) + F_57(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_16(x) + F_54(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_63(x))
Eq(F_59(x), F_10(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_20(x) + F_60(x))
Eq(F_63(x), F_54(x) + F_64(x))
Eq(F_64(x), 2*F_29(x) + F_65(x) + F_84(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_12(x) + F_68(x))
Eq(F_71(x), 2*F_29(x) + F_72(x) + F_80(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_71(x) + F_74(x))
Eq(F_74(x), F_29(x) + F_75(x) + F_79(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_12(x))
Eq(F_78(x), F_74(x))
Eq(F_79(x), F_10(x)*F_12(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_68(x))
Eq(F_83(x), F_71(x))
Eq(F_84(x), F_12(x)*F_63(x))
Eq(F_85(x), F_118(x) + F_86(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), F_10(x)*F_19(x))
Eq(F_88(x), F_107(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_86(x) + F_92(x))
Eq(F_92(x), F_10(x)*F_93(x))
Eq(F_93(x), F_14(x) + F_94(x))
Eq(F_94(x), F_87(x) + F_95(x))
Eq(F_95(x), F_101(x) + F_96(x))
Eq(F_96(x), F_29(x) + F_97(x) + F_99(x))
Eq(F_97(x), F_12(x)*F_98(x))
Eq(F_98(x), F_10(x) + F_96(x))
Eq(F_99(x), F_100(x)*F_12(x))
Eq(F_100(x), F_10(x) + F_96(x))
Eq(F_101(x), F_102(x) + F_106(x) + F_29(x))
Eq(F_102(x), F_10(x)*F_103(x)*F_12(x))
Eq(F_103(x), F_104(x) + F_12(x))
Eq(F_104(x), F_105(x) + F_29(x) + F_79(x))
Eq(F_105(x), F_103(x)*F_12(x))
Eq(F_106(x), F_12(x)*F_95(x))
Eq(F_107(x), F_108(x) + F_117(x) + F_29(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_112(x))
Eq(F_110(x), F_10(x)*F_111(x))
Eq(F_111(x), F_12(x) + F_74(x))
Eq(F_112(x), F_113(x) + F_115(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_10(x)**2*F_12(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_12(x)*F_13(x)*F_71(x))
Eq(F_117(x), F_12(x)*F_88(x))
Eq(F_118(x), F_119(x) + F_127(x))
Eq(F_119(x), F_120(x) + F_125(x))
Eq(F_120(x), F_121(x) + F_123(x) + F_29(x))
Eq(F_121(x), F_12(x)*F_122(x))
Eq(F_122(x), F_10(x) + F_120(x))
Eq(F_123(x), F_12(x)*F_124(x))
Eq(F_124(x), F_10(x) + F_120(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_10(x)**2*F_20(x))
Eq(F_127(x), F_128(x) + F_132(x))
Eq(F_128(x), F_129(x) + F_130(x) + F_29(x))
Eq(F_129(x), F_10(x)*F_12(x)*F_122(x))
Eq(F_130(x), F_12(x)*F_131(x))
Eq(F_131(x), F_128(x) + F_96(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_10(x)*F_101(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_col_placements_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "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, 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, 3, 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, 3, 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"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": 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