0123_0132_0213_1023_1230_3012
Counting sequence:
1, 1, 2, 6, 18, 54, 158, 478, 1514, 4998, 17008, 59109, 208498, 743628, 2675532, 9696492, 35360174, 129648632, 477644650, 1767272485, 6564135052, 24466290202, 91482600560, 343059672691, 1289904242038, 4861946553754, 18367353317488, 69533551311713, 263747952389204, 1002242217683424, 3814986503760386, 14544636041923882, 55534064881409714, 212336130419297658, 812944042161142456, 3116285494925762669, 11959798385890321266, 45950804324670065696, 176733862787084886100, 680425371730102301425, 2622127042276696786932, 10113918591638229304882, 39044429911904979799230, 150853479205086218661831, 583300119592998095918664, 2257117854077250343074162, 8740328711533177062685216, 33868773757191052828875759, 131327898242169375093063054, 509552245179617153612110998, 1978261657756160678796332008, 7684785670514316425960859029, 29869166945772626016044999708, 116157871455782434357186451548, 451959718027953471620144676666, 1759414616608818871271647626989, 6852456927844873498001361359356, 26700952856774851904976091534136, 104088460289122304034680892302580, 405944995127576985732556887451587, 1583850964596120042689868796584838, 6182127958584855650492090308816128, 24139737743045626825719564025386772, 94295850558771979787948499887059396, 368479169875816659479030263133303934, 1440418573150919668872524229604264032, 5632681584560312734993971261629261306, 22033725021956517463358642505197423429, 86218923998960285726185786110621654764, 337485502510215975556784028793119598946, 1321422108420282270489942557975211017472, 5175569924646105559418940810118108113623, 20276890389709399862928999565162664843726, 79463489365077377841208239245380335045338, 311496878311103321137536294128748223949232, 1221395654430378811828760726230932286814497, 4790408930363303911328386215227773706908084, 18793142726809884575211361290143424595092552, 73745243611532458459690151872536117886994450, 289450081175264899454283846058435435313823595, 1136359577947336271931632877051500913364631312, 4462290049988320482463241297581911308246027712, 17526585015616776834735140518038267217839545860, 68854441132780194707888052034867036849174808811, 270557451039395118028642463289489567708304109734, 1063353702922273835973036658043995849716925748292, 4180080073556524734514695828171747850710206395836, 16435314834665426797069144960764245926642867725279, 64633260585762914370496637486148381638238267574424, 254224158304000796523953440778845207045379381568366, 1000134600800354781929399250536547624496849831700342, 3935312233584004685417853572763358829867252431205723, 15487357822491889407128326963778358312241540620653856, 60960876535340415751462563580829673292290559151321058, 239993345518077005168915776623476762486829267224809792, 944973797977428207852605870454939660718100028215242087, 3721443204405954385563870541379246763070924407095483134, 14657929356129575437016877846657032928955241930596748302, 57743358069601357782187700608042856604624436314170255000, 227508830794229349661819540395688854393887674270651542045, 896519947090131496687170070074100633129287217897269900972
Generating function in Maple syntax:
1/2*(-(x^2+x-1)*(x-1)^4*(1-4*x)^(1/2)-4*x^8+8*x^7-x^6-x^5-x^4+6*x^3-9*x^2+5*x-1)/x/(x^2+x-1)/(x-1)^4
Generating function in latex syntax:
\frac{-\left(x^{2}+x -1\right) \left(x -1\right)^{4} \sqrt{1-4 x}-4 x^{8}+8 x^{7}-x^{6}-x^{5}-x^{4}+6 x^{3}-9 x^{2}+5 x -1}{2 x \left(x^{2}+x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-2*x**8 + 4*x**7 - x**6/2 - x**5/2 - x**4/2 + 3*x**3 - 9*x**2/2 + 5*x/2 + sqrt(1 - 4*x)*(x - 1)**4*(-x**2 - x + 1)/2 - 1/2)/(x*(x - 1)**4*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(x^2+x-1)^2*(x-1)^8*F(x)^2+(x^2+x-1)*(4*x^8-8*x^7+x^6+x^5+x^4-6*x^3+9*x^2-5*x+1)*(x-1)^4*F(x)+4*x^15-16*x^14+18*x^13-x^12-8*x^11-3*x^10+46*x^9-103*x^8+113*x^7-38*x^6-77*x^5+133*x^4-101*x^3+43*x^2-10*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{8} F \! \left(x \right)^{2}+\left(x^{2}+x -1\right) \left(4 x^{8}-8 x^{7}+x^{6}+x^{5}+x^{4}-6 x^{3}+9 x^{2}-5 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+4 x^{15}-16 x^{14}+18 x^{13}-x^{12}-8 x^{11}-3 x^{10}+46 x^{9}-103 x^{8}+113 x^{7}-38 x^{6}-77 x^{5}+133 x^{4}-101 x^{3}+43 x^{2}-10 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 18
a(5) = 54
a(6) = 158
a(7) = 478
a(8) = 1514
a(9) = 4998
a(10) = 17008
a(11) = 59109
a(n+5) = 2*(2*n+1)/(6+n)*a(n)+(7*n+10)/(6+n)*a(1+n)-2*(3*n+8)/(6+n)*a(n+2)-(24+7*n)/(6+n)*a(n+3)+2*(3*n+14)/(6+n)*a(n+4)-1/2*(n^4-12*n^3-11*n^2+126*n+80)/(6+n), n >= 12
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) = 18
a \! \left(5\right) = 54
a \! \left(6\right) = 158
a \! \left(7\right) = 478
a \! \left(8\right) = 1514
a \! \left(9\right) = 4998
a \! \left(10\right) = 17008
a \! \left(11\right) = 59109
a \! \left(n +5\right) = \frac{2 \left(2 n +1\right) a \! \left(n \right)}{6+n}+\frac{\left(7 n +10\right) a \! \left(1+n \right)}{6+n}-\frac{2 \left(3 n +8\right) a \! \left(n +2\right)}{6+n}-\frac{\left(24+7 n \right) a \! \left(n +3\right)}{6+n}+\frac{2 \left(3 n +14\right) a \! \left(n +4\right)}{6+n}-\frac{n^{4}-12 n^{3}-11 n^{2}+126 n +80}{2 \left(6+n \right)}, \quad n \geq 12
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/22061/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[1,x]+F[110,x]+F[4,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[1,x]+F[108,x]+F[46,x]+F[6,x]
F[6,x] = F[12,x]*F[7,x]
F[7,x] = F[21,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[10,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[20,x]
F[15,x] = 0
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[12,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[10,x]*F[12,x]
F[20,x] = F[12,x]*F[13,x]
F[21,x] = F[22,x]+F[27,x]
F[22,x] = F[10,x]+F[23,x]
F[23,x] = F[15,x]+F[24,x]+F[26,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[10,x]+F[23,x]
F[26,x] = F[12,x]*F[22,x]
F[27,x] = F[23,x]+F[28,x]
F[28,x] = F[15,x]+F[29,x]+F[37,x]+F[45,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[10,x]+F[31,x]
F[34,x] = 2*F[15,x]+F[29,x]+F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[23,x]+F[34,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[12,x]+F[39,x]
F[42,x] = F[43,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[18,x]+F[42,x]
F[45,x] = F[12,x]*F[27,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x,1]
F[48,x,k[0]] = F[1,x]+F[106,x,k[0]]+F[49,x,k[0]]+F[96,x,k[0]]+F[98,x,k[0]]
F[49,x,k[0]] = F[12,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[67,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[60,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[9,x]
F[53,x,k[0]] = F[54,x,k[0]]+F[58,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]*F[57,x,k[0]]
F[56,x,k[0]] = F[1,x]+F[54,x,k[0]]
F[57,x,k[0]] = k[0]*x
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[12,x]*F[53,x,k[0]]
F[60,x,k[0]] = F[13,x]+F[61,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[65,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[57,x,k[0]]*F[64,x,k[0]]
F[64,x,k[0]] = F[10,x]+F[62,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[12,x]*F[61,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[79,x,k[0]]
F[68,x,k[0]] = F[22,x]+F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[75,x,k[0]]
F[70,x,k[0]] = F[15,x]+F[71,x,k[0]]+F[73,x,k[0]]
F[71,x,k[0]] = F[12,x]*F[72,x,k[0]]
F[72,x,k[0]] = F[54,x,k[0]]+F[70,x,k[0]]
F[73,x,k[0]] = F[57,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = F[10,x]+F[70,x,k[0]]
F[75,x,k[0]] = 2*F[15,x]+F[76,x,k[0]]+F[78,x,k[0]]
F[76,x,k[0]] = F[12,x]*F[77,x,k[0]]
F[77,x,k[0]] = F[58,x,k[0]]+F[75,x,k[0]]
F[78,x,k[0]] = F[12,x]*F[69,x,k[0]]
F[79,x,k[0]] = F[27,x]+F[80,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]+F[86,x,k[0]]
F[81,x,k[0]] = 2*F[15,x]+F[82,x,k[0]]+F[84,x,k[0]]
F[82,x,k[0]] = F[12,x]*F[83,x,k[0]]
F[83,x,k[0]] = F[62,x,k[0]]+F[81,x,k[0]]
F[84,x,k[0]] = F[57,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[23,x]+F[81,x,k[0]]
F[86,x,k[0]] = 3*F[15,x]+F[87,x,k[0]]+F[95,x,k[0]]
F[87,x,k[0]] = F[12,x]*F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]+F[92,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[12,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[62,x,k[0]]+F[89,x,k[0]]
F[92,x,k[0]] = 3*F[15,x]+F[87,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[12,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[81,x,k[0]]+F[92,x,k[0]]
F[95,x,k[0]] = F[12,x]*F[80,x,k[0]]
F[96,x,k[0]] = F[12,x]*F[97,x,k[0]]
F[97,x,k[0]] = 1/(-1+k[0])*(F[48,x,k[0]]*k[0]-F[48,x,1])
F[98,x,k[0]] = F[57,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[104,x,k[0]]+F[98,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[12,x]
F[101,x,k[0]] = F[102,x,k[0]]+F[103,x,k[0]]
F[102,x,k[0]] = F[56,x,k[0]]+F[64,x,k[0]]
F[103,x,k[0]] = F[74,x,k[0]]+F[85,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[12,x]
F[105,x,k[0]] = 1/(-1+k[0])*(F[99,x,k[0]]*k[0]-F[99,x,1])
F[106,x,k[0]] = F[107,x,k[0]]*F[12,x]
F[107,x,k[0]] = 1/(-1+k[0])*(F[99,x,k[0]]*k[0]-F[99,x,1])
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[99,x,1]
F[110,x] = F[111,x]*F[12,x]
F[111,x] = F[112,x]+F[131,x]
F[112,x] = F[113,x]+F[121,x]
F[113,x] = F[1,x]+F[114,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[1,x]+F[12,x]
F[118,x] = F[114,x]+F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[114,x]*F[12,x]
F[121,x] = F[12,x]+F[122,x]
F[122,x] = F[123,x]
F[123,x] = F[12,x]*F[124,x]
F[124,x] = F[125,x]+F[128,x]
F[125,x] = F[12,x]+F[126,x]
F[126,x] = F[127,x]
F[127,x] = x^2
F[128,x] = F[122,x]+F[129,x]
F[129,x] = F[130,x]
F[130,x] = F[12,x]*F[122,x]
F[131,x] = F[132,x]+F[152,x]
F[132,x] = F[114,x]+F[133,x]
F[133,x] = F[134,x]+F[146,x]+F[15,x]
F[134,x] = F[12,x]*F[135,x]
F[135,x] = F[136,x]+F[140,x]
F[136,x] = F[10,x]+F[137,x]
F[137,x] = F[138,x]
F[138,x] = F[12,x]*F[139,x]
F[139,x] = F[12,x]+F[137,x]
F[140,x] = F[141,x]+F[142,x]
F[141,x] = F[134,x]+F[15,x]+F[26,x]
F[142,x] = F[143,x]
F[143,x] = F[12,x]*F[144,x]
F[144,x] = F[145,x]+F[18,x]
F[145,x] = F[143,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = F[10,x]+F[39,x]
F[149,x] = F[150,x]+F[151,x]
F[150,x] = F[146,x]+F[15,x]+F[24,x]
F[151,x] = F[43,x]
F[152,x] = F[119,x]+F[153,x]
F[153,x] = F[154,x]
F[154,x] = F[12,x]*F[155,x]
F[155,x] = F[156,x]+F[157,x]
F[156,x] = F[18,x]
F[157,x] = F[154,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_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{110}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{108}\! \left(x \right)+F_{46}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{21}\! \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_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{12}\! \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_{19}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{15}\! \left(x \right)+F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{37}\! \left(x \right)+F_{45}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{18}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{106}\! \left(x , y\right)+F_{49}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = y x
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{70}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{76}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = -\frac{-y F_{48}\! \left(x , y\right)+F_{48}\! \left(x , 1\right)}{-1+y}
F_{98}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{103}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{105}\! \left(x , y\right) = -\frac{-y F_{99}\! \left(x , y\right)+F_{99}\! \left(x , 1\right)}{-1+y}
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{107}\! \left(x , y\right) = -\frac{-y F_{99}\! \left(x , y\right)+F_{99}\! \left(x , 1\right)}{-1+y}
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{99}\! \left(x , 1\right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{12}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{131}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{121}\! \left(x \right)
F_{113}\! \left(x \right) = F_{1}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \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_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{118}\! \left(x \right) = F_{114}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{121}\! \left(x \right) = F_{12}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \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_{128}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = x^{2}
F_{128}\! \left(x \right) = F_{122}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{152}\! \left(x \right)
F_{132}\! \left(x \right) = F_{114}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{146}\! \left(x \right)+F_{15}\! \left(x \right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right) F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{140}\! \left(x \right)
F_{136}\! \left(x \right) = F_{10}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{12}\! \left(x \right) F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{12}\! \left(x \right)+F_{137}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{142}\! \left(x \right)
F_{141}\! \left(x \right) = F_{134}\! \left(x \right)+F_{15}\! \left(x \right)+F_{26}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{12}\! \left(x \right) F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{18}\! \left(x \right)
F_{145}\! \left(x \right) = F_{143}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = F_{10}\! \left(x \right)+F_{39}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{151}\! \left(x \right)
F_{150}\! \left(x \right) = F_{146}\! \left(x \right)+F_{15}\! \left(x \right)+F_{24}\! \left(x \right)
F_{151}\! \left(x \right) = F_{43}\! \left(x \right)
F_{152}\! \left(x \right) = F_{119}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{12}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{156}\! \left(x \right) = F_{18}\! \left(x \right)
F_{157}\! \left(x \right) = F_{154}\! \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_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_110(x) + F_4(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_108(x) + F_46(x) + F_6(x))
Eq(F_6(x), F_12(x)*F_7(x))
Eq(F_7(x), F_21(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_10(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_20(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_12(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_10(x)*F_12(x))
Eq(F_20(x), F_12(x)*F_13(x))
Eq(F_21(x), F_22(x) + F_27(x))
Eq(F_22(x), F_10(x) + F_23(x))
Eq(F_23(x), F_15(x) + F_24(x) + F_26(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_10(x) + F_23(x))
Eq(F_26(x), F_12(x)*F_22(x))
Eq(F_27(x), F_23(x) + F_28(x))
Eq(F_28(x), F_15(x) + F_29(x) + F_37(x) + F_45(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_10(x) + F_31(x))
Eq(F_34(x), 2*F_15(x) + F_29(x) + F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_23(x) + F_34(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_12(x) + F_39(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_18(x) + F_42(x))
Eq(F_45(x), F_12(x)*F_27(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x, 1))
Eq(F_48(x, k_0), F_1(x) + F_106(x, k_0) + F_49(x, k_0) + F_96(x, k_0) + F_98(x, k_0))
Eq(F_49(x, k_0), F_12(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_67(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_60(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_9(x))
Eq(F_53(x, k_0), F_54(x, k_0) + F_58(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0)*F_57(x, k_0))
Eq(F_56(x, k_0), F_1(x) + F_54(x, k_0))
Eq(F_57(x, k_0), k_0*x)
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_12(x)*F_53(x, k_0))
Eq(F_60(x, k_0), F_13(x) + F_61(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_65(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_57(x, k_0)*F_64(x, k_0))
Eq(F_64(x, k_0), F_10(x) + F_62(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_12(x)*F_61(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_79(x, k_0))
Eq(F_68(x, k_0), F_22(x) + F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_75(x, k_0))
Eq(F_70(x, k_0), F_15(x) + F_71(x, k_0) + F_73(x, k_0))
Eq(F_71(x, k_0), F_12(x)*F_72(x, k_0))
Eq(F_72(x, k_0), F_54(x, k_0) + F_70(x, k_0))
Eq(F_73(x, k_0), F_57(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), F_10(x) + F_70(x, k_0))
Eq(F_75(x, k_0), 2*F_15(x) + F_76(x, k_0) + F_78(x, k_0))
Eq(F_76(x, k_0), F_12(x)*F_77(x, k_0))
Eq(F_77(x, k_0), F_58(x, k_0) + F_75(x, k_0))
Eq(F_78(x, k_0), F_12(x)*F_69(x, k_0))
Eq(F_79(x, k_0), F_27(x) + F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0) + F_86(x, k_0))
Eq(F_81(x, k_0), 2*F_15(x) + F_82(x, k_0) + F_84(x, k_0))
Eq(F_82(x, k_0), F_12(x)*F_83(x, k_0))
Eq(F_83(x, k_0), F_62(x, k_0) + F_81(x, k_0))
Eq(F_84(x, k_0), F_57(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_23(x) + F_81(x, k_0))
Eq(F_86(x, k_0), 3*F_15(x) + F_87(x, k_0) + F_95(x, k_0))
Eq(F_87(x, k_0), F_12(x)*F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0) + F_92(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_12(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_62(x, k_0) + F_89(x, k_0))
Eq(F_92(x, k_0), 3*F_15(x) + F_87(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_12(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_81(x, k_0) + F_92(x, k_0))
Eq(F_95(x, k_0), F_12(x)*F_80(x, k_0))
Eq(F_96(x, k_0), F_12(x)*F_97(x, k_0))
Eq(F_97(x, k_0), (k_0*F_48(x, k_0) - F_48(x, 1))/(k_0 - 1))
Eq(F_98(x, k_0), F_57(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_1(x) + F_100(x, k_0) + F_104(x, k_0) + F_98(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_12(x))
Eq(F_101(x, k_0), F_102(x, k_0) + F_103(x, k_0))
Eq(F_102(x, k_0), F_56(x, k_0) + F_64(x, k_0))
Eq(F_103(x, k_0), F_74(x, k_0) + F_85(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_12(x))
Eq(F_105(x, k_0), (k_0*F_99(x, k_0) - F_99(x, 1))/(k_0 - 1))
Eq(F_106(x, k_0), F_107(x, k_0)*F_12(x))
Eq(F_107(x, k_0), (-k_0*F_99(x, k_0) + F_99(x, 1))/(1 - k_0))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_99(x, 1))
Eq(F_110(x), F_111(x)*F_12(x))
Eq(F_111(x), F_112(x) + F_131(x))
Eq(F_112(x), F_113(x) + F_121(x))
Eq(F_113(x), F_1(x) + F_114(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_1(x) + F_12(x))
Eq(F_118(x), F_114(x) + F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_114(x)*F_12(x))
Eq(F_121(x), F_12(x) + F_122(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_12(x)*F_124(x))
Eq(F_124(x), F_125(x) + F_128(x))
Eq(F_125(x), F_12(x) + F_126(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), x**2)
Eq(F_128(x), F_122(x) + F_129(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_12(x)*F_122(x))
Eq(F_131(x), F_132(x) + F_152(x))
Eq(F_132(x), F_114(x) + F_133(x))
Eq(F_133(x), F_134(x) + F_146(x) + F_15(x))
Eq(F_134(x), F_12(x)*F_135(x))
Eq(F_135(x), F_136(x) + F_140(x))
Eq(F_136(x), F_10(x) + F_137(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_12(x)*F_139(x))
Eq(F_139(x), F_12(x) + F_137(x))
Eq(F_140(x), F_141(x) + F_142(x))
Eq(F_141(x), F_134(x) + F_15(x) + F_26(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_12(x)*F_144(x))
Eq(F_144(x), F_145(x) + F_18(x))
Eq(F_145(x), F_143(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), F_10(x) + F_39(x))
Eq(F_149(x), F_150(x) + F_151(x))
Eq(F_150(x), F_146(x) + F_15(x) + F_24(x))
Eq(F_151(x), F_43(x))
Eq(F_152(x), F_119(x) + F_153(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_12(x)*F_155(x))
Eq(F_155(x), F_156(x) + F_157(x))
Eq(F_156(x), F_18(x))
Eq(F_157(x), F_154(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "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:
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