0132_0213_0231_1203_3012
Counting sequence:
1, 1, 2, 6, 19, 57, 170, 522, 1666, 5503, 18665, 64565, 226675, 805079, 2886349, 10429496, 37938987, 138814037, 510506426, 1885992459, 6995876756, 26045499437, 97288623042, 364503234551, 1369426451678, 5157937341873, 19472744778544, 73674239279245, 279301683210104, 1060816037120873, 4036088361472984, 15381055390086542, 58704581340356290, 224376752327712839, 858750400398394521, 3290831921286466545, 12625929407456719107, 48496644641083680991, 186476766635039917745, 717758777227053653913, 2765354990250570154837, 10664029790028560371611, 41159572303168256889275, 158994353145685349693259, 614663471073310300876043, 2378058777591195057543347, 9207100210691663313203691, 35671782434403071355569465, 138297968673514160866571099, 536517648506784362199383655, 2082659767589564184637977893, 8089250532463730513592101807, 31437212748869611469861039709, 122240826291994329747318441983, 475571957317518092545963307405, 1851124468388260975652339337471, 7208859758552272903931636314361, 28086761622332024336208093231599, 109479762280087837557340951065633, 426929749178963160781206839361299, 1665570539327558865100692821956709, 6500513135761876282038736959965511, 25380752759850457717939371913940777, 99135255612110546420795492976458816, 387358704085775863025631136439785035, 1514101841339216892982202304093500645, 5920367779850482969929693605742068858, 23157388357906684338650315605572980499, 90609436432155309199714807285377476468, 354646836154951947990298187845525571165, 1388524641997372114443542091808023405690, 5438036685897279000642270114576480886643, 21303848832885562888454672414654731632974, 83482974555359934684115595295068377225833, 327233917346740063860813555259532897660660, 1283027734723973037917744052850625894016605, 5031853919082245695972549003564007478052548, 19739278858797744692578921464958865121202529, 77453841654374289816915624371123295000152828, 303990716481339437681658892746876674371830015, 1193385377526195441145988907280751010289702660, 4685992527187858549816311233832436963237010413, 18404351008571685425292631280667840318353200754, 72299467138747766618101587267256531627198133393, 284081583183568302809358540809512770247343787250, 1116457662395450680492300157484919390252334998565, 4388645607697900257183174821719375828800022943698, 17254635582986371329034038035928143877284039494289, 67852541341736467196906822351770637509990073949918, 266876037637578795500445527629982094314246767143525, 1049867112189711016443193690357188889239346450043430, 4130841985927741286023736598984402766374947239295773, 16256258843578372215275534888095690202962950027778154, 63985081612062366187053685406254560571339932751519773, 251890234271711504119200654176320361762281790649893830, 991783420085328230297380526098054817779860017895453375, 3905653843903305211641521888020094310072745450754704958, 15382983519104979767786171137407380060629034951603470929, 60597665405638923531728922743092886820465396212123409488, 238747217955296567337629454687062937425537412570519904325, 940776613288731386619326188221859418090329259332564250040
Generating function in Maple syntax:
1/2/x*(-1+(1-4*x)^(1/2))*(x^4+3*x^2-3*x+1)/(x-1)^3
Generating function in latex syntax:
\frac{\left(-1+\sqrt{1-4 x}\right) \left(x^{4}+3 x^{2}-3 x +1\right)}{2 x \left(x -1\right)^{3}}
Generating function in sympy syntax:
(sqrt(1 - 4*x) - 1)*(x**4 + 3*x**2 - 3*x + 1)/(2*x*(x - 1)**3)
Implicit equation for the generating function in Maple syntax:
x*(x-1)^6*F(x)^2+(x^4+3*x^2-3*x+1)*(x-1)^3*F(x)+(x^4+3*x^2-3*x+1)^2 = 0
Implicit equation for the generating function in latex syntax:
x \left(x -1\right)^{6} F \! \left(x \right)^{2}+\left(x^{4}+3 x^{2}-3 x +1\right) \left(x -1\right)^{3} F \! \left(x \right)+\left(x^{4}+3 x^{2}-3 x +1\right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 57
a(6) = 170
a(7) = 522
a(8) = 1666
a(n+6) = -2*(-1+2*n)/(7+n)*a(n)+(-9+5*n)/(7+n)*a(1+n)-(41+13*n)/(7+n)*a(n+2)+9*(11+3*n)/(7+n)*a(n+3)-2*(51+11*n)/(7+n)*a(n+4)+2*(23+4*n)/(7+n)*a(n+5)+4*n/(7+n), n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 57
a \! \left(6\right) = 170
a \! \left(7\right) = 522
a \! \left(8\right) = 1666
a \! \left(n +6\right) = -\frac{2 \left(-1+2 n \right) a \! \left(n \right)}{7+n}+\frac{\left(-9+5 n \right) a \! \left(1+n \right)}{7+n}-\frac{\left(41+13 n \right) a \! \left(n +2\right)}{7+n}+\frac{9 \left(11+3 n \right) a \! \left(n +3\right)}{7+n}-\frac{2 \left(51+11 n \right) a \! \left(n +4\right)}{7+n}+\frac{2 \left(23+4 n \right) a \! \left(n +5\right)}{7+n}+\frac{4 n}{7+n}, \quad n \geq 9
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21571/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[20,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[82,x]
F[4,x] = F[20,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[79,x,k[0]]+F[81,x,k[0]]
F[7,x,k[0]] = F[20,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[35,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[31,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[15,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[11,x,k[0]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[16,x]+F[27,x,k[0]]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[20,x]
F[18,x] = F[19,x]+F[21,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = x
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[20,x]*F[24,x]
F[24,x] = F[1,x]+F[22,x]
F[25,x] = F[26,x]
F[26,x] = F[20,x]*F[22,x]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[14,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[22,x]+F[30,x,k[0]]
F[30,x,k[0]] = F[28,x,k[0]]
F[31,x,k[0]] = F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[20,x]*F[34,x]
F[34,x] = F[1,x]+F[32,x]
F[35,x,k[0]] = F[36,x,k[0]]+F[70,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[43,x,k[0]]
F[37,x,k[0]] = F[22,x]+F[38,x,k[0]]
F[38,x,k[0]] = F[39,x]+F[40,x,k[0]]+F[42,x,k[0]]
F[39,x] = 0
F[40,x,k[0]] = F[20,x]*F[41,x,k[0]]
F[41,x,k[0]] = F[12,x,k[0]]+F[38,x,k[0]]
F[42,x,k[0]] = F[14,x,k[0]]*F[37,x,k[0]]
F[43,x,k[0]] = F[44,x]+F[62,x,k[0]]
F[44,x] = F[39,x]+F[45,x]+F[47,x]
F[45,x] = F[20,x]*F[46,x]
F[46,x] = F[16,x]+F[44,x]
F[47,x] = F[20,x]*F[48,x]
F[48,x] = F[49,x]+F[53,x]
F[49,x] = F[22,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[20,x]*F[52,x]
F[52,x] = F[20,x]+F[50,x]
F[53,x] = F[54,x]+F[59,x]
F[54,x] = F[39,x]+F[55,x]+F[57,x]
F[55,x] = F[20,x]*F[56,x]
F[56,x] = F[22,x]+F[54,x]
F[57,x] = F[20,x]*F[58,x]
F[58,x] = F[22,x]+F[54,x]
F[59,x] = F[60,x]
F[60,x] = F[20,x]*F[61,x]
F[61,x] = F[25,x]+F[59,x]
F[62,x,k[0]] = 2*F[39,x]+F[63,x,k[0]]+F[65,x,k[0]]
F[63,x,k[0]] = F[20,x]*F[64,x,k[0]]
F[64,x,k[0]] = F[27,x,k[0]]+F[62,x,k[0]]
F[65,x,k[0]] = F[14,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[54,x]+F[67,x,k[0]]
F[67,x,k[0]] = 2*F[39,x]+F[65,x,k[0]]+F[68,x,k[0]]
F[68,x,k[0]] = F[20,x]*F[69,x,k[0]]
F[69,x,k[0]] = F[30,x,k[0]]+F[67,x,k[0]]
F[70,x,k[0]] = F[71,x]
F[71,x] = F[39,x]+F[72,x]+F[74,x]
F[72,x] = F[20,x]*F[73,x]
F[73,x] = F[32,x]+F[71,x]
F[74,x] = F[20,x]*F[75,x]
F[75,x] = F[22,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[20,x]*F[78,x]
F[78,x] = F[32,x]+F[76,x]
F[79,x,k[0]] = F[20,x]*F[80,x,k[0]]
F[80,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[81,x,k[0]] = F[14,x,k[0]]*F[6,x,k[0]]
F[82,x] = F[20,x]*F[83,x]
F[83,x] = F[84,x]+F[87,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[1,x]+F[16,x]
F[86,x] = F[32,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[22,x]+F[44,x]
F[89,x] = F[71,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_{20}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{82}\! \left(x \right)
F_{4}\! \left(x \right) = F_{20}\! \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_{7}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{20}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{39}\! \left(x \right) = 0
F_{40}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{44}\! \left(x \right) = F_{39}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{49}\! \left(x \right) = F_{22}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{20}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{20}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{54}\! \left(x \right) = F_{39}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{22}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{20}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{22}\! \left(x \right)+F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{20}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{25}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x , y\right) = 2 F_{39}\! \left(x \right)+F_{63}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{54}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = 2 F_{39}\! \left(x \right)+F_{65}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{39}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{20}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{32}\! \left(x \right)+F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{20}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{22}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{20}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{32}\! \left(x \right)+F_{76}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{81}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{82}\! \left(x \right) = F_{20}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{87}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{86}\! \left(x \right) = F_{32}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{22}\! \left(x \right)+F_{44}\! \left(x \right)
F_{89}\! \left(x \right) = F_{71}\! \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_20(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_82(x))
Eq(F_4(x), F_20(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_79(x, k_0) + F_81(x, k_0))
Eq(F_7(x, k_0), F_20(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_35(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_31(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_15(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_11(x, k_0)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_16(x) + F_27(x, k_0))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_20(x))
Eq(F_18(x), F_19(x) + F_21(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), x)
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_20(x)*F_24(x))
Eq(F_24(x), F_1(x) + F_22(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_20(x)*F_22(x))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_14(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_22(x) + F_30(x, k_0))
Eq(F_30(x, k_0), F_28(x, k_0))
Eq(F_31(x, k_0), F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_20(x)*F_34(x))
Eq(F_34(x), F_1(x) + F_32(x))
Eq(F_35(x, k_0), F_36(x, k_0) + F_70(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_43(x, k_0))
Eq(F_37(x, k_0), F_22(x) + F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x) + F_40(x, k_0) + F_42(x, k_0))
Eq(F_39(x), 0)
Eq(F_40(x, k_0), F_20(x)*F_41(x, k_0))
Eq(F_41(x, k_0), F_12(x, k_0) + F_38(x, k_0))
Eq(F_42(x, k_0), F_14(x, k_0)*F_37(x, k_0))
Eq(F_43(x, k_0), F_44(x) + F_62(x, k_0))
Eq(F_44(x), F_39(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_20(x)*F_46(x))
Eq(F_46(x), F_16(x) + F_44(x))
Eq(F_47(x), F_20(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_53(x))
Eq(F_49(x), F_22(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_20(x)*F_52(x))
Eq(F_52(x), F_20(x) + F_50(x))
Eq(F_53(x), F_54(x) + F_59(x))
Eq(F_54(x), F_39(x) + F_55(x) + F_57(x))
Eq(F_55(x), F_20(x)*F_56(x))
Eq(F_56(x), F_22(x) + F_54(x))
Eq(F_57(x), F_20(x)*F_58(x))
Eq(F_58(x), F_22(x) + F_54(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_20(x)*F_61(x))
Eq(F_61(x), F_25(x) + F_59(x))
Eq(F_62(x, k_0), 2*F_39(x) + F_63(x, k_0) + F_65(x, k_0))
Eq(F_63(x, k_0), F_20(x)*F_64(x, k_0))
Eq(F_64(x, k_0), F_27(x, k_0) + F_62(x, k_0))
Eq(F_65(x, k_0), F_14(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_54(x) + F_67(x, k_0))
Eq(F_67(x, k_0), 2*F_39(x) + F_65(x, k_0) + F_68(x, k_0))
Eq(F_68(x, k_0), F_20(x)*F_69(x, k_0))
Eq(F_69(x, k_0), F_30(x, k_0) + F_67(x, k_0))
Eq(F_70(x, k_0), F_71(x))
Eq(F_71(x), F_39(x) + F_72(x) + F_74(x))
Eq(F_72(x), F_20(x)*F_73(x))
Eq(F_73(x), F_32(x) + F_71(x))
Eq(F_74(x), F_20(x)*F_75(x))
Eq(F_75(x), F_22(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_20(x)*F_78(x))
Eq(F_78(x), F_32(x) + F_76(x))
Eq(F_79(x, k_0), F_20(x)*F_80(x, k_0))
Eq(F_80(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_81(x, k_0), F_14(x, k_0)*F_6(x, k_0))
Eq(F_82(x), F_20(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_87(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_1(x) + F_16(x))
Eq(F_86(x), F_32(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_22(x) + F_44(x))
Eq(F_89(x), F_71(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 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], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "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, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 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": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[2, 1], [2, 1], [2, 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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 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"}}, {"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": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 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], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "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, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 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": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 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