0123_0132_0231_1023_3012
Counting sequence:
1, 1, 2, 6, 19, 60, 189, 602, 1955, 6486, 21950, 75568, 263927, 932893, 3330710, 11992965, 43497827, 158757252, 582613417, 2148459331, 7956847537, 29582008341, 110362737695, 413033160243, 1550221935637, 5833699792393, 22006115626725, 83197575752219, 315191155903161, 1196380732015395, 4549247146870641, 17327379515234028, 66100236122945271, 252527000140328018, 966071069703610122, 3700598167088480472, 14192683454549301363, 54495122547999389165, 209471258243639138942, 806009604144857149446, 3104431869696189116989, 11968206420846846489015, 46180799804441742696078, 178345059548027309524376, 689304391823669202243135, 2666217416664114062471407, 10320480069510062396902816, 39977007892906957260890200, 154957934736370221779766825, 601033114878451668749399435, 2332666575621826392011191944, 9058701113482044754873296826, 35198822206605620851234169383, 136845268160839287387112503811, 532306707488104086826549513038, 2071648811080951115308385326976, 8066485817869558075383866207601, 31423827574522946932350245565001, 122470948791224649245730784909876, 477528792919250354403758969636662, 1862739219166561730034890028161355, 7269163291869486351669386937973883, 28378590207645627559132016499854262, 110832127632851122465298690002478641, 433015741684008356380313880736381315, 1692387487177466074758636408268713028, 6616818321551406960665969403773245593, 25878988275397267234574605468718345099, 101248746645389146075557847152948026049, 396252567048389091133396635120648642349, 1551281333559847809041414750948931428311, 6074929399468187343722737976549534821159, 23796900846414927113461481474209062338541, 93244779108423687282113208444516850799453, 365468717937287819539316715320420812265577, 1432828455520363447458917126995729118733247, 5618926606513591575207044123620828698937201, 22040664692431600191395863613348848565767195, 86477931293114543249279469094496713584411381, 339384803665654479475706017109779143594585833, 1332242591105942457326741132539701215527763669, 5230888710956322914739525768860018464017103665, 20543120400580425265038909113473343781048250043, 80696317487673259486237817454528421609138388977, 317055353362058617945087154770733940854271042485, 1245972079287950911946635417318100208744277559683, 4897463761934725956687666480398081678193589928123, 19254036109774844611818927340940273881492457851509, 75710822273439196962560492372286242136963575161289, 297767875271748759600772418334161811971957806295599, 1171330769286083887918721986429417348623971299542491, 4608517984460017560033558488611612359202736504535369, 18135156185842725679111471914602981019161852614914301, 71376936269376622059321077163440921489583718857719023, 280976150635081376192389394546272779317239178694036207, 1106252801520968321194592306624994133898028082713775447, 4356233435518471443061284588953816889768451514719766981, 17156877621805380612833777011118780383926608496873407385, 67582502809972336754418539833037266561511516846985382661, 266255017115479554984992396358917061345988637358240842003, 1049125602194320047754545472507028168092000011171420249369
Generating function in Maple syntax:
1/2*((x^5-3*x^4+9*x^3-10*x^2+5*x-1)*(1-4*x)^(1/2)+2*x^6-3*x^5+7*x^4-11*x^3+10*x^2-5*x+1)/x/(2*x-1)/(x-1)^3
Generating function in latex syntax:
\frac{\left(x^{5}-3 x^{4}+9 x^{3}-10 x^{2}+5 x -1\right) \sqrt{1-4 x}+2 x^{6}-3 x^{5}+7 x^{4}-11 x^{3}+10 x^{2}-5 x +1}{2 x \left(2 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(x**6 - 3*x**5/2 + 7*x**4/2 - 11*x**3/2 + 5*x**2 - 5*x/2 + sqrt(1 - 4*x)*(x**5 - 3*x**4 + 9*x**3 - 10*x**2 + 5*x - 1)/2 + 1/2)/(x*(x - 1)**3*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^6*F(x)^2-(x^5-x^4+3*x^3-4*x^2+3*x-1)*(2*x-1)^2*(x-1)^3*F(x)+x^11-2*x^10+3*x^9+7*x^8-42*x^7+111*x^6-176*x^5+175*x^4-111*x^3+44*x^2-10*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)^{2}-\left(x^{5}-x^{4}+3 x^{3}-4 x^{2}+3 x -1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3} F \! \left(x \right)+x^{11}-2 x^{10}+3 x^{9}+7 x^{8}-42 x^{7}+111 x^{6}-176 x^{5}+175 x^{4}-111 x^{3}+44 x^{2}-10 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 60
a(6) = 189
a(7) = 602
a(8) = 1955
a(9) = 6486
a(10) = 21950
a(11) = 75568
a(n+8) = -4*(-1+2*n)/(9+n)*a(n)+2*(8+19*n)/(9+n)*a(1+n)-(265+121*n)/(9+n)*a(n+2)+4*(193+57*n)/(9+n)*a(n+3)-2*(548+123*n)/(9+n)*a(n+4)+(873+157*n)/(9+n)*a(n+5)-(395+59*n)/(9+n)*a(n+6)+2*(47+6*n)/(9+n)*a(n+7)+2*(n-2)/(9+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) = 19
a \! \left(5\right) = 60
a \! \left(6\right) = 189
a \! \left(7\right) = 602
a \! \left(8\right) = 1955
a \! \left(9\right) = 6486
a \! \left(10\right) = 21950
a \! \left(11\right) = 75568
a \! \left(n +8\right) = -\frac{4 \left(-1+2 n \right) a \! \left(n \right)}{9+n}+\frac{2 \left(8+19 n \right) a \! \left(1+n \right)}{9+n}-\frac{\left(265+121 n \right) a \! \left(n +2\right)}{9+n}+\frac{4 \left(193+57 n \right) a \! \left(n +3\right)}{9+n}-\frac{2 \left(548+123 n \right) a \! \left(n +4\right)}{9+n}+\frac{\left(873+157 n \right) a \! \left(n +5\right)}{9+n}-\frac{\left(395+59 n \right) a \! \left(n +6\right)}{9+n}+\frac{2 \left(47+6 n \right) a \! \left(n +7\right)}{9+n}+\frac{2 n -4}{9+n}, \quad n \geq 12
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21498/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[111,x]+F[4,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[108,x,k[0]]+F[110,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[21,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[106,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[43,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[16,x,k[0]]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[12,x,k[0]]*F[15,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[17,x]+F[31,x,k[0]]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[21,x]
F[19,x] = F[20,x]+F[22,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = x
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[24,x]
F[24,x] = F[21,x]*F[25,x]
F[25,x] = F[1,x]+F[24,x]
F[26,x] = F[27,x]+F[28,x]+F[30,x]
F[27,x] = 0
F[28,x] = F[21,x]*F[29,x]
F[29,x] = F[21,x]+F[26,x]
F[30,x] = F[21,x]*F[23,x]
F[31,x,k[0]] = F[27,x]+F[32,x,k[0]]+F[40,x,k[0]]
F[32,x,k[0]] = F[21,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[15,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[27,x]+F[37,x,k[0]]+F[39,x,k[0]]
F[37,x,k[0]] = F[21,x]*F[38,x,k[0]]
F[38,x,k[0]] = F[15,x,k[0]]+F[36,x,k[0]]
F[39,x,k[0]] = F[15,x,k[0]]*F[23,x]
F[40,x,k[0]] = F[15,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[23,x]+F[42,x,k[0]]
F[42,x,k[0]] = F[40,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[57,x,k[0]]
F[44,x,k[0]] = F[45,x]+F[51,x,k[0]]
F[45,x] = F[46,x]
F[46,x] = F[21,x]*F[47,x]
F[47,x] = F[25,x]+F[48,x]
F[48,x] = F[45,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[21,x]*F[48,x]
F[51,x,k[0]] = F[27,x]+F[52,x,k[0]]+F[56,x,k[0]]
F[52,x,k[0]] = F[21,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[55,x,k[0]]
F[54,x,k[0]] = F[13,x,k[0]]
F[55,x,k[0]] = F[51,x,k[0]]
F[56,x,k[0]] = F[15,x,k[0]]*F[44,x,k[0]]
F[57,x,k[0]] = F[58,x]+F[82,x,k[0]]
F[58,x] = F[27,x]+F[59,x]+F[66,x]
F[59,x] = F[21,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[23,x]
F[62,x] = F[63,x]
F[63,x] = F[27,x]+F[59,x]+F[64,x]
F[64,x] = F[21,x]*F[65,x]
F[65,x] = F[45,x]+F[63,x]
F[66,x] = F[21,x]*F[67,x]
F[67,x] = F[68,x]+F[74,x]
F[68,x] = F[45,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[21,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[21,x]
F[73,x] = F[69,x]
F[74,x] = F[63,x]+F[75,x]
F[75,x] = 2*F[27,x]+F[76,x]+F[80,x]
F[76,x] = F[21,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[30,x]
F[79,x] = F[76,x]
F[80,x] = F[21,x]*F[81,x]
F[81,x] = F[69,x]+F[75,x]
F[82,x,k[0]] = F[27,x]+F[83,x,k[0]]+F[88,x,k[0]]+F[90,x,k[0]]
F[83,x,k[0]] = F[21,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[86,x,k[0]]
F[85,x,k[0]] = F[42,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = 2*F[27,x]+F[83,x,k[0]]+F[88,x,k[0]]
F[88,x,k[0]] = F[15,x,k[0]]*F[89,x,k[0]]
F[89,x,k[0]] = F[63,x]+F[87,x,k[0]]
F[90,x,k[0]] = F[21,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]+F[98,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[21,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]+F[97,x,k[0]]
F[96,x,k[0]] = F[15,x,k[0]]
F[97,x,k[0]] = F[93,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = 2*F[27,x]+F[100,x,k[0]]+F[104,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[21,x]
F[101,x,k[0]] = F[102,x,k[0]]+F[103,x,k[0]]
F[102,x,k[0]] = F[39,x,k[0]]
F[103,x,k[0]] = F[100,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[21,x]
F[105,x,k[0]] = F[93,x,k[0]]+F[99,x,k[0]]
F[106,x] = F[107,x]*F[21,x]*F[25,x]
F[107,x] = F[1,x]+F[46,x]
F[108,x,k[0]] = F[109,x,k[0]]*F[21,x]
F[109,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[110,x,k[0]] = F[15,x,k[0]]*F[6,x,k[0]]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[21,x]
F[113,x] = F[114,x]+F[117,x]
F[114,x] = F[115,x]+F[116,x]
F[115,x] = F[1,x]+F[17,x]
F[116,x] = F[45,x]+F[58,x]
F[117,x] = F[107,x]*F[21,x]*F[25,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_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{111}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{108}\! \left(x , y\right)+F_{110}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{106}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{21}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{23}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x \right)+F_{51}\! \left(x , y\right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{21}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{25}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{45}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{21}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{52}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{58}\! \left(x \right) = F_{27}\! \left(x \right)+F_{59}\! \left(x \right)+F_{66}\! \left(x \right)
F_{59}\! \left(x \right) = F_{21}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{27}\! \left(x \right)+F_{59}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{21}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{45}\! \left(x \right)+F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{21}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{74}\! \left(x \right)
F_{68}\! \left(x \right) = F_{45}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{21}\! \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) = F_{21}\! \left(x \right)
F_{73}\! \left(x \right) = F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{63}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{21}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{30}\! \left(x \right)
F_{79}\! \left(x \right) = F_{76}\! \left(x \right)
F_{80}\! \left(x \right) = F_{21}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{82}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{83}\! \left(x , y\right)+F_{88}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{83}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{63}\! \left(x \right)+F_{87}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{21}\! \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_{39}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{100}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{93}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{21}\! \left(x \right) F_{25}\! \left(x \right)
F_{107}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{109}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{110}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{21}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{117}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)
F_{115}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{116}\! \left(x \right) = F_{45}\! \left(x \right)+F_{58}\! \left(x \right)
F_{117}\! \left(x \right) = F_{107}\! \left(x \right) F_{21}\! \left(x \right) F_{25}\! \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_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_111(x) + F_4(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_108(x, k_0) + F_110(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_21(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_106(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_43(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_16(x, k_0))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_12(x, k_0)*F_15(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_17(x) + F_31(x, k_0))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_21(x))
Eq(F_19(x), F_20(x) + F_22(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), x)
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_21(x)*F_25(x))
Eq(F_25(x), F_1(x) + F_24(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_30(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_21(x)*F_29(x))
Eq(F_29(x), F_21(x) + F_26(x))
Eq(F_30(x), F_21(x)*F_23(x))
Eq(F_31(x, k_0), F_27(x) + F_32(x, k_0) + F_40(x, k_0))
Eq(F_32(x, k_0), F_21(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_15(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_27(x) + F_37(x, k_0) + F_39(x, k_0))
Eq(F_37(x, k_0), F_21(x)*F_38(x, k_0))
Eq(F_38(x, k_0), F_15(x, k_0) + F_36(x, k_0))
Eq(F_39(x, k_0), F_15(x, k_0)*F_23(x))
Eq(F_40(x, k_0), F_15(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_23(x) + F_42(x, k_0))
Eq(F_42(x, k_0), F_40(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_57(x, k_0))
Eq(F_44(x, k_0), F_45(x) + F_51(x, k_0))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_21(x)*F_47(x))
Eq(F_47(x), F_25(x) + F_48(x))
Eq(F_48(x), F_45(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_21(x)*F_48(x))
Eq(F_51(x, k_0), F_27(x) + F_52(x, k_0) + F_56(x, k_0))
Eq(F_52(x, k_0), F_21(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_55(x, k_0))
Eq(F_54(x, k_0), F_13(x, k_0))
Eq(F_55(x, k_0), F_51(x, k_0))
Eq(F_56(x, k_0), F_15(x, k_0)*F_44(x, k_0))
Eq(F_57(x, k_0), F_58(x) + F_82(x, k_0))
Eq(F_58(x), F_27(x) + F_59(x) + F_66(x))
Eq(F_59(x), F_21(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_23(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_27(x) + F_59(x) + F_64(x))
Eq(F_64(x), F_21(x)*F_65(x))
Eq(F_65(x), F_45(x) + F_63(x))
Eq(F_66(x), F_21(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_74(x))
Eq(F_68(x), F_45(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_21(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_21(x))
Eq(F_73(x), F_69(x))
Eq(F_74(x), F_63(x) + F_75(x))
Eq(F_75(x), 2*F_27(x) + F_76(x) + F_80(x))
Eq(F_76(x), F_21(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_30(x))
Eq(F_79(x), F_76(x))
Eq(F_80(x), F_21(x)*F_81(x))
Eq(F_81(x), F_69(x) + F_75(x))
Eq(F_82(x, k_0), F_27(x) + F_83(x, k_0) + F_88(x, k_0) + F_90(x, k_0))
Eq(F_83(x, k_0), F_21(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_86(x, k_0))
Eq(F_85(x, k_0), F_42(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), 2*F_27(x) + F_83(x, k_0) + F_88(x, k_0))
Eq(F_88(x, k_0), F_15(x, k_0)*F_89(x, k_0))
Eq(F_89(x, k_0), F_63(x) + F_87(x, k_0))
Eq(F_90(x, k_0), F_21(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0) + F_98(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_21(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0) + F_97(x, k_0))
Eq(F_96(x, k_0), F_15(x, k_0))
Eq(F_97(x, k_0), F_93(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_104(x, k_0) + 2*F_27(x))
Eq(F_100(x, k_0), F_101(x, k_0)*F_21(x))
Eq(F_101(x, k_0), F_102(x, k_0) + F_103(x, k_0))
Eq(F_102(x, k_0), F_39(x, k_0))
Eq(F_103(x, k_0), F_100(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_21(x))
Eq(F_105(x, k_0), F_93(x, k_0) + F_99(x, k_0))
Eq(F_106(x), F_107(x)*F_21(x)*F_25(x))
Eq(F_107(x), F_1(x) + F_46(x))
Eq(F_108(x, k_0), F_109(x, k_0)*F_21(x))
Eq(F_109(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_110(x, k_0), F_15(x, k_0)*F_6(x, k_0))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_21(x))
Eq(F_113(x), F_114(x) + F_117(x))
Eq(F_114(x), F_115(x) + F_116(x))
Eq(F_115(x), F_1(x) + F_17(x))
Eq(F_116(x), F_45(x) + F_58(x))
Eq(F_117(x), F_107(x)*F_21(x)*F_25(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 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