01234_01324_01342_02134_02314_02341_03124_03142_03214_03241_03412_03421_30124_30142_30214_30241_30412_30421_34012_34021
Counting sequence:
1, 1, 2, 6, 24, 100, 400, 1526, 5600, 19944, 69408, 237226, 799216, 2661308, 8776976, 28714206, 93300672, 301392592, 968682304, 3099626066, 9879746768, 31382108196, 99375452592, 313814790406, 988511766304, 3106741678520, 9743852563040, 30502457048826, 95320102780080, 297398570349964, 926510631296848, 2882476923066926, 8956266393600896, 27795307127744928, 86165447371545216, 266834924374534306, 825520528493233552, 2551608868768461812, 7879968490531407344, 24315331192991764566, 74972270880606874848, 230995644821593275016, 711223431553853590432, 2188379787028293695306, 6729267840384103113584, 20680188963448021934940, 63517723226027296609680, 194984638702723768288126, 598248323217281312330560, 1834628191049542703567984, 5623534237482461898788288, 17229551705730362037328626, 52765502097602965088298576, 161527047235170432100676548, 494272764534847706623057456, 1511893162097055950459626406, 4622904091777713542404982432, 14130386091810792098802739032, 43176179724901359508190556384, 131883603523183085753956615066, 402716003615130394138100538928, 1229343589982422823419145409836, 3751617507358939854024271032272, 11445612734312986634877924352206, 34909118839649766966058320516864, 106444198429086333768467031319360, 324483121017679323288314158040320, 988900940244317382557755375919426, 3013057552306827279239852252257040, 9178236851642181019395609968474004, 27951903139091788177167579216943728, 85107287169771395036350164938222326, 259076594766802866919403135382492256, 788493984072875826780888045262256168, 2399274551536031519593941487953713696, 7299201452560311398902139390007190506, 22201737751537594161800328687750147312, 67517613436182781270148649095017024252, 205290040853258377943620799337512529424, 624081724193905311788250680084245377566, 1896879977484106620352644338296506339008, 5764544347159492218253064812678123312656, 17515346285599994330807499638714770178112, 53211178589164537229493234132814685961106, 161628954964587276817543547277713533576144, 490873122485042830675525454929465726631780, 1490578140228971502366667360994405955254960, 4525610739008443557463088185435310987142726, 13738461171989917862164149091330345916159520, 41700270380863515233188353334400543793868024, 126555471737271830794395283095102683880163168, 384030396995859347977161528382356277860948026, 1165183136339709611332381642080903649693781936, 3534825245075523537437776136329595672313283788, 10722303243395754725111102117820201736433913936, 32520392254694816518678387637096370467380426606, 98621624337607106595973927076479449375570328192, 299046215733389290927545114353575446445384117472, 906682675361871786241119423690269803088943726464, 2748680110570727099178038675473704138118749252066, 8331936585167516519056613564658325276099089875088
Generating function in Maple syntax:
(9*x^5-29*x^4+44*x^3-30*x^2+9*x-1)/(2*x-1)/(3*x-1)^2/(x-1)^2
Generating function in latex syntax:
\frac{9 x^{5}-29 x^{4}+44 x^{3}-30 x^{2}+9 x -1}{\left(2 x -1\right) \left(3 x -1\right)^{2} \left(x -1\right)^{2}}
Generating function in sympy syntax:
(9*x**5 - 29*x**4 + 44*x**3 - 30*x**2 + 9*x - 1)/((x - 1)**2*(2*x - 1)*(3*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(3*x-1)^2*(x-1)^2*F(x)-9*x^5+29*x^4-44*x^3+30*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(3 x -1\right)^{2} \left(x -1\right)^{2} F \! \left(x \right)-9 x^{5}+29 x^{4}-44 x^{3}+30 x^{2}-9 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,2^(-1+n)+1/6*(n-3)*3^n+1/2*n+1/2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 2^{-1+n}+\frac{\left(n -3\right) 3^{n}}{6}+\frac{n}{2}+\frac{1}{2} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 100
a(n+3) = 18*a(n)-21*a(n+1)+8*a(n+2)-2*n+2, n >= 6
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 100
a{\left(n + 3 \right)} = - 2 \left(n - 1\right) + 18 a{\left(n \right)} - 21 a{\left(n + 1 \right)} + 8 a{\left(n + 2 \right)}, \quad n \geq 6
Specification 1
Strategy pack name: regular_insertion_encoding_left
Tree: http://permpal.com/tree/25808/
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[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[32,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[19,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[1,x]+F[6,x]
F[10,x] = F[11,x]+F[23,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[19,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[16,x]+F[20,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[19,x]
F[18,x] = F[1,x]+F[16,x]
F[19,x] = x
F[20,x] = F[21,x]
F[21,x] = F[19,x]*F[22,x]
F[22,x] = F[11,x]+F[20,x]
F[23,x] = F[24,x]+F[25,x]+F[28,x]
F[24,x] = 0
F[25,x] = F[19,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[23,x]+F[6,x]
F[28,x] = F[19,x]*F[29,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[16,x]
F[31,x] = F[20,x]
F[32,x] = F[24,x]+F[33,x]+F[94,x]
F[33,x] = F[19,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[2,x]+F[32,x]
F[36,x] = F[37,x]+F[58,x]
F[37,x] = F[24,x]+F[38,x]+F[55,x]
F[38,x] = F[19,x]*F[39,x]
F[39,x] = F[40,x]+F[44,x]
F[40,x] = F[16,x]+F[41,x]
F[41,x] = F[24,x]+F[38,x]+F[42,x]
F[42,x] = F[19,x]*F[43,x]
F[43,x] = F[11,x]+F[41,x]
F[44,x] = F[45,x]+F[50,x]
F[45,x] = F[24,x]+F[46,x]+F[48,x]
F[46,x] = F[19,x]*F[47,x]
F[47,x] = F[16,x]+F[45,x]
F[48,x] = F[19,x]*F[49,x]
F[49,x] = F[16,x]+F[45,x]
F[50,x] = 2*F[24,x]+F[51,x]+F[53,x]
F[51,x] = F[19,x]*F[52,x]
F[52,x] = F[41,x]+F[50,x]
F[53,x] = F[19,x]*F[54,x]
F[54,x] = F[20,x]+F[50,x]
F[55,x] = F[19,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[11,x]+F[37,x]
F[58,x] = F[24,x]+F[59,x]+F[76,x]+F[88,x]
F[59,x] = F[19,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]+F[67,x]
F[62,x] = F[24,x]+F[63,x]+F[74,x]
F[63,x] = F[19,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[16,x]+F[62,x]
F[66,x] = F[41,x]+F[67,x]
F[67,x] = F[24,x]+F[59,x]+F[68,x]+F[72,x]
F[68,x] = F[19,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[45,x]
F[71,x] = F[50,x]
F[72,x] = F[19,x]*F[73,x]
F[73,x] = F[23,x]+F[67,x]
F[74,x] = F[19,x]*F[75,x]
F[75,x] = F[6,x]+F[62,x]
F[76,x] = F[19,x]*F[77,x]
F[77,x] = F[78,x]+F[83,x]
F[78,x] = F[79,x]
F[79,x] = F[24,x]+F[46,x]+F[80,x]
F[80,x] = F[19,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[16,x]+F[79,x]
F[83,x] = F[84,x]
F[84,x] = 2*F[24,x]+F[51,x]+F[85,x]
F[85,x] = F[19,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[20,x]+F[84,x]
F[88,x] = F[19,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[23,x]+F[91,x]
F[91,x] = F[24,x]+F[59,x]+F[68,x]+F[92,x]
F[92,x] = F[19,x]*F[93,x]
F[93,x] = F[90,x]
F[94,x] = F[19,x]*F[95,x]
F[95,x] = F[100,x]+F[96,x]
F[96,x] = F[6,x]+F[97,x]
F[97,x] = F[24,x]+F[63,x]+F[98,x]
F[98,x] = F[19,x]*F[99,x]
F[99,x] = F[96,x]
F[100,x] = F[101,x]+F[105,x]
F[101,x] = F[102,x]+F[24,x]+F[28,x]
F[102,x] = F[103,x]*F[19,x]
F[103,x] = F[104,x]
F[104,x] = F[101,x]+F[6,x]
F[105,x] = F[106,x]+F[112,x]+F[24,x]+F[76,x]
F[106,x] = F[107,x]*F[19,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]+F[62,x]
F[109,x] = F[106,x]+F[110,x]+F[24,x]+F[68,x]
F[110,x] = F[111,x]*F[19,x]
F[111,x] = F[101,x]+F[109,x]
F[112,x] = F[113,x]*F[19,x]
F[113,x] = F[114,x]
F[114,x] = F[101,x]+F[115,x]
F[115,x] = F[106,x]+F[116,x]+F[24,x]+F[68,x]
F[116,x] = F[117,x]*F[19,x]
F[117,x] = F[114,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_{19}\! \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_{32}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right)+F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)+F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right)
F_{31}\! \left(x \right) = F_{20}\! \left(x \right)
F_{32}\! \left(x \right) = F_{24}\! \left(x \right)+F_{33}\! \left(x \right)+F_{94}\! \left(x \right)
F_{33}\! \left(x \right) = F_{19}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{58}\! \left(x \right)
F_{37}\! \left(x \right) = F_{24}\! \left(x \right)+F_{38}\! \left(x \right)+F_{55}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{24}\! \left(x \right)+F_{38}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{19}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{11}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{50}\! \left(x \right)
F_{45}\! \left(x \right) = F_{24}\! \left(x \right)+F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{16}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{19}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right)+F_{45}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{19}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{41}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{19}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{20}\! \left(x \right)+F_{50}\! \left(x \right)
F_{55}\! \left(x \right) = F_{19}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right)+F_{37}\! \left(x \right)
F_{58}\! \left(x \right) = F_{24}\! \left(x \right)+F_{59}\! \left(x \right)+F_{76}\! \left(x \right)+F_{88}\! \left(x \right)
F_{59}\! \left(x \right) = F_{19}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{67}\! \left(x \right)
F_{62}\! \left(x \right) = F_{24}\! \left(x \right)+F_{63}\! \left(x \right)+F_{74}\! \left(x \right)
F_{63}\! \left(x \right) = F_{19}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{16}\! \left(x \right)+F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{41}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{24}\! \left(x \right)+F_{59}\! \left(x \right)+F_{68}\! \left(x \right)+F_{72}\! \left(x \right)
F_{68}\! \left(x \right) = F_{19}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{45}\! \left(x \right)
F_{71}\! \left(x \right) = F_{50}\! \left(x \right)
F_{72}\! \left(x \right) = F_{19}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{23}\! \left(x \right)+F_{67}\! \left(x \right)
F_{74}\! \left(x \right) = F_{19}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{6}\! \left(x \right)+F_{62}\! \left(x \right)
F_{76}\! \left(x \right) = F_{19}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{83}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{24}\! \left(x \right)+F_{46}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{16}\! \left(x \right)+F_{79}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{51}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{19}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right)+F_{84}\! \left(x \right)
F_{88}\! \left(x \right) = F_{19}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{23}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{24}\! \left(x \right)+F_{59}\! \left(x \right)+F_{68}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{19}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{90}\! \left(x \right)
F_{94}\! \left(x \right) = F_{19}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{100}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{6}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{24}\! \left(x \right)+F_{63}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{19}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{96}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{105}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{19}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{101}\! \left(x \right)+F_{6}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{112}\! \left(x \right)+F_{24}\! \left(x \right)+F_{76}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{19}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{62}\! \left(x \right)
F_{109}\! \left(x \right) = F_{106}\! \left(x \right)+F_{110}\! \left(x \right)+F_{24}\! \left(x \right)+F_{68}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{19}\! \left(x \right)
F_{111}\! \left(x \right) = F_{101}\! \left(x \right)+F_{109}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{19}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{101}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{106}\! \left(x \right)+F_{116}\! \left(x \right)+F_{24}\! \left(x \right)+F_{68}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{19}\! \left(x \right)
F_{117}\! \left(x \right) = F_{114}\! \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_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_32(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_19(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_6(x))
Eq(F_10(x), F_11(x) + F_23(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_19(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_16(x) + F_20(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_19(x))
Eq(F_18(x), F_1(x) + F_16(x))
Eq(F_19(x), x)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_19(x)*F_22(x))
Eq(F_22(x), F_11(x) + F_20(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_28(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_19(x)*F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_23(x) + F_6(x))
Eq(F_28(x), F_19(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_16(x))
Eq(F_31(x), F_20(x))
Eq(F_32(x), F_24(x) + F_33(x) + F_94(x))
Eq(F_33(x), F_19(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_2(x) + F_32(x))
Eq(F_36(x), F_37(x) + F_58(x))
Eq(F_37(x), F_24(x) + F_38(x) + F_55(x))
Eq(F_38(x), F_19(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_44(x))
Eq(F_40(x), F_16(x) + F_41(x))
Eq(F_41(x), F_24(x) + F_38(x) + F_42(x))
Eq(F_42(x), F_19(x)*F_43(x))
Eq(F_43(x), F_11(x) + F_41(x))
Eq(F_44(x), F_45(x) + F_50(x))
Eq(F_45(x), F_24(x) + F_46(x) + F_48(x))
Eq(F_46(x), F_19(x)*F_47(x))
Eq(F_47(x), F_16(x) + F_45(x))
Eq(F_48(x), F_19(x)*F_49(x))
Eq(F_49(x), F_16(x) + F_45(x))
Eq(F_50(x), 2*F_24(x) + F_51(x) + F_53(x))
Eq(F_51(x), F_19(x)*F_52(x))
Eq(F_52(x), F_41(x) + F_50(x))
Eq(F_53(x), F_19(x)*F_54(x))
Eq(F_54(x), F_20(x) + F_50(x))
Eq(F_55(x), F_19(x)*F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x) + F_37(x))
Eq(F_58(x), F_24(x) + F_59(x) + F_76(x) + F_88(x))
Eq(F_59(x), F_19(x)*F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_62(x) + F_67(x))
Eq(F_62(x), F_24(x) + F_63(x) + F_74(x))
Eq(F_63(x), F_19(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_16(x) + F_62(x))
Eq(F_66(x), F_41(x) + F_67(x))
Eq(F_67(x), F_24(x) + F_59(x) + F_68(x) + F_72(x))
Eq(F_68(x), F_19(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_45(x))
Eq(F_71(x), F_50(x))
Eq(F_72(x), F_19(x)*F_73(x))
Eq(F_73(x), F_23(x) + F_67(x))
Eq(F_74(x), F_19(x)*F_75(x))
Eq(F_75(x), F_6(x) + F_62(x))
Eq(F_76(x), F_19(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_83(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_24(x) + F_46(x) + F_80(x))
Eq(F_80(x), F_19(x)*F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_16(x) + F_79(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), 2*F_24(x) + F_51(x) + F_85(x))
Eq(F_85(x), F_19(x)*F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_20(x) + F_84(x))
Eq(F_88(x), F_19(x)*F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_23(x) + F_91(x))
Eq(F_91(x), F_24(x) + F_59(x) + F_68(x) + F_92(x))
Eq(F_92(x), F_19(x)*F_93(x))
Eq(F_93(x), F_90(x))
Eq(F_94(x), F_19(x)*F_95(x))
Eq(F_95(x), F_100(x) + F_96(x))
Eq(F_96(x), F_6(x) + F_97(x))
Eq(F_97(x), F_24(x) + F_63(x) + F_98(x))
Eq(F_98(x), F_19(x)*F_99(x))
Eq(F_99(x), F_96(x))
Eq(F_100(x), F_101(x) + F_105(x))
Eq(F_101(x), F_102(x) + F_24(x) + F_28(x))
Eq(F_102(x), F_103(x)*F_19(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_101(x) + F_6(x))
Eq(F_105(x), F_106(x) + F_112(x) + F_24(x) + F_76(x))
Eq(F_106(x), F_107(x)*F_19(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x) + F_62(x))
Eq(F_109(x), F_106(x) + F_110(x) + F_24(x) + F_68(x))
Eq(F_110(x), F_111(x)*F_19(x))
Eq(F_111(x), F_101(x) + F_109(x))
Eq(F_112(x), F_113(x)*F_19(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_101(x) + F_115(x))
Eq(F_115(x), F_106(x) + F_116(x) + F_24(x) + F_68(x))
Eq(F_116(x), F_117(x)*F_19(x))
Eq(F_117(x), F_114(x))
Pack JSON:
{"name": "regular_insertion_encoding_left", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": true, "maxreqlen": 1, "extra_basis": [], "one_cell_only": true}], "inferral_strats": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"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, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], 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