0132_0231_1023_1320_3021
Counting sequence:
1, 1, 2, 6, 19, 51, 127, 313, 777, 1948, 4925, 12532, 32046, 82266, 211864, 547097, 1416016, 3672165, 9538909, 24813343, 64622427, 168463930, 439523975, 1147486330, 2997429744, 7833268296, 20478257602, 53551172543, 140070402082, 366441929523, 958802401255, 2509025749717, 6566328690381, 17185933789096, 44983151177249, 117746339872912, 308220434960706, 806841950564550, 2112155092876924, 5529314090420213, 14475151523223172, 37894834809190545, 99206672844754945, 259719686166934555, 679941115661863119, 1780080571074470566, 4660253318561553227, 12200582627586943798, 31941296652106277412, 83622902708452865748, 218926584640508231110, 573155162363211562427, 1500535454380661749366, 3928444163904355917951, 10284782682108593759659, 26925874609023847451377, 70492781472267885933921, 184552348210589871345460, 483164015461522222723589, 1264939193770818531328108, 3311652539030218330785942, 8670016333649609361117810, 22698392210520561514817440, 59425151651000790631980305, 155577045160428865126705144, 407305948089719161935876861, 1066340726474673830449563877, 2791716083760349739736399703, 7308807225046784190979419267, 19134704982637448400786652498, 50095306486933708072840577615, 131151211969406481793236058162, 343358324329984372963031348376, 898923750690369955818509079456, 2353412906785624226758445251594, 6161314927165204378630019749367, 16130531788526800596760588843786, 42230280263687637545474873872395, 110560308648358625824440641743279, 289450644963588534531660978872653, 757791624787918101046691569053237, 1983924226453409083297755114937600, 5193981048603237914499342225644585, 13598018907267046464053979814931080, 35600075648717153630466356431345194, 93202207989318455823145293316147806, 244006548218897370810955302016482052, 638817436464274118914462911382657133, 1672445760762890207263459512731385772, 4378519844992655538981050754613647273, 11463113772532251668776128939918555145, 30010821469199764359312540309169422547, 78569350628180999940636564208463329911, 205697230401416410020636624223605415486, 538522340547905094227530907208397836179, 1409869791185353630854828604756228374382, 3691087032893027374683414541494668729676, 9663391307260995765809763528046742455980, 25299086888419542707817431538183891428494, 66233869357046894407471359035382404420723, 173402521180799857573625735381319881033182
Generating function in Maple syntax:
(4*x^10-15*x^9+5*x^8+27*x^7-33*x^6+38*x^5-62*x^4+62*x^3-33*x^2+9*x-1)/(x^2-3*x+1)/(2*x-1)^2/(x-1)^3
Generating function in latex syntax:
\frac{4 x^{10}-15 x^{9}+5 x^{8}+27 x^{7}-33 x^{6}+38 x^{5}-62 x^{4}+62 x^{3}-33 x^{2}+9 x -1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(4*x**10 - 15*x**9 + 5*x**8 + 27*x**7 - 33*x**6 + 38*x**5 - 62*x**4 + 62*x**3 - 33*x**2 + 9*x - 1)/((x - 1)**3*(2*x - 1)**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(2*x-1)^2*(x-1)^3*F(x)+4*x^10-15*x^9+5*x^8+27*x^7-33*x^6+38*x^5-62*x^4+62*x^3-33*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3} F \! \left(x \right)+4 x^{10}-15 x^{9}+5 x^{8}+27 x^{7}-33 x^{6}+38 x^{5}-62 x^{4}+62 x^{3}-33 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,79/16,n = 1,19/4,n = 2,13/4,n = 3,1,0)+1/80*(-8*5^(1/2)+40)*(3/2-1/2*5^(1/2))^(-n)+1/80*(8*5^(1/2)+40)*(3/2+1/2*5^(1/2))^(-n)+1/80*(5*n+5)*2^n+1/2*n^2-1/2*n-5
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}\frac{79}{16} & n =0 \\ \frac{19}{4} & n =1 \\ \frac{13}{4} & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(-8 \sqrt{5}+40\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{80}+\frac{\left(8 \sqrt{5}+40\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{80}+\frac{\left(5 n +5\right) 2^{n}}{80}+\frac{n^{2}}{2}-\frac{n}{2}-5
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(6) = 127
a(7) = 313
a(8) = 777
a(9) = 1948
a(10) = 4925
a(n+4) = -1/2*n^2-4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)+3/2*n+7, n >= 11
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) = 51
a \! \left(6\right) = 127
a \! \left(7\right) = 313
a \! \left(8\right) = 777
a \! \left(9\right) = 1948
a \! \left(10\right) = 4925
a \! \left(n +4\right) = -\frac{n^{2}}{2}-4 a \! \left(n \right)+16 a \! \left(n +1\right)-17 a \! \left(n +2\right)+7 a \! \left(n +3\right)+\frac{3 n}{2}+7, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18797/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[21,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]+F[4,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[15,x]
F[21,x] = F[22,x]+F[36,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[10,x]+F[25,x]
F[25,x] = F[22,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]+F[35,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[17,x]+F[30,x]
F[30,x] = F[31,x]+F[33,x]
F[31,x] = F[27,x]+F[28,x]+F[32,x]
F[32,x] = F[22,x]*F[4,x]
F[33,x] = F[34,x]
F[34,x] = F[30,x]*F[4,x]
F[35,x] = F[25,x]*F[4,x]
F[36,x] = F[27,x]+F[37,x]+F[97,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[47,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[1,x]+F[40,x]
F[43,x] = F[19,x]+F[27,x]+F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[11,x]+F[46,x]
F[46,x] = F[19,x]
F[47,x] = F[48,x]+F[58,x]
F[48,x] = F[27,x]+F[37,x]+F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[22,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[17,x]+F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[52,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[54,x]
F[58,x] = F[27,x]+F[59,x]+F[72,x]+F[95,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[68,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[4,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[18,x]
F[68,x] = F[69,x]
F[69,x] = 2*F[27,x]+F[59,x]+F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[55,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[94,x]
F[74,x] = F[27,x]+F[32,x]+F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[80,x]
F[77,x] = F[4,x]+F[78,x]
F[78,x] = F[19,x]+F[27,x]+F[79,x]
F[79,x] = F[11,x]*F[4,x]
F[80,x] = F[74,x]+F[81,x]
F[81,x] = F[27,x]+F[72,x]+F[82,x]+F[92,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[89,x]
F[84,x] = F[85,x]+F[87,x]
F[85,x] = F[86,x]
F[86,x] = x^2
F[87,x] = F[88,x]
F[88,x] = F[18,x]*F[4,x]
F[89,x] = F[90,x]
F[90,x] = 2*F[27,x]+F[82,x]+F[91,x]
F[91,x] = F[4,x]*F[55,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[52,x]
F[94,x] = F[72,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[93,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[102,x]+F[99,x]
F[99,x] = F[100,x]+F[22,x]
F[100,x] = F[101,x]+F[27,x]+F[75,x]
F[101,x] = F[4,x]*F[99,x]
F[102,x] = F[52,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{21}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{36}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{35}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{17}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{33}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)+F_{97}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{47}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{19}\! \left(x \right)+F_{27}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{58}\! \left(x \right)
F_{48}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{22}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{17}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{52}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{58}\! \left(x \right) = F_{27}\! \left(x \right)+F_{59}\! \left(x \right)+F_{72}\! \left(x \right)+F_{95}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{18}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{59}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{55}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{94}\! \left(x \right)
F_{74}\! \left(x \right) = F_{27}\! \left(x \right)+F_{32}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{19}\! \left(x \right)+F_{27}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{80}\! \left(x \right) = F_{74}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{27}\! \left(x \right)+F_{72}\! \left(x \right)+F_{82}\! \left(x \right)+F_{92}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{89}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = x^{2}
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{82}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{52}\! \left(x \right)
F_{94}\! \left(x \right) = F_{72}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{93}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{102}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{22}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{27}\! \left(x \right)+F_{75}\! \left(x \right)
F_{101}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{102}\! \left(x \right) = F_{52}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_21(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x) + F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_15(x))
Eq(F_21(x), F_22(x) + F_36(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_10(x) + F_25(x))
Eq(F_25(x), F_22(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_35(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_17(x) + F_30(x))
Eq(F_30(x), F_31(x) + F_33(x))
Eq(F_31(x), F_27(x) + F_28(x) + F_32(x))
Eq(F_32(x), F_22(x)*F_4(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_30(x)*F_4(x))
Eq(F_35(x), F_25(x)*F_4(x))
Eq(F_36(x), F_27(x) + F_37(x) + F_97(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_47(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_1(x) + F_40(x))
Eq(F_43(x), F_19(x) + F_27(x) + F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_11(x) + F_46(x))
Eq(F_46(x), F_19(x))
Eq(F_47(x), F_48(x) + F_58(x))
Eq(F_48(x), F_27(x) + F_37(x) + F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_22(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_17(x) + F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_52(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_54(x))
Eq(F_58(x), F_27(x) + F_59(x) + F_72(x) + F_95(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_68(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_4(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_18(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), 2*F_27(x) + F_59(x) + F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_55(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_94(x))
Eq(F_74(x), F_27(x) + F_32(x) + F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_80(x))
Eq(F_77(x), F_4(x) + F_78(x))
Eq(F_78(x), F_19(x) + F_27(x) + F_79(x))
Eq(F_79(x), F_11(x)*F_4(x))
Eq(F_80(x), F_74(x) + F_81(x))
Eq(F_81(x), F_27(x) + F_72(x) + F_82(x) + F_92(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_89(x))
Eq(F_84(x), F_85(x) + F_87(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), x**2)
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_18(x)*F_4(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), 2*F_27(x) + F_82(x) + F_91(x))
Eq(F_91(x), F_4(x)*F_55(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_52(x))
Eq(F_94(x), F_72(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_93(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_102(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_22(x))
Eq(F_100(x), F_101(x) + F_27(x) + F_75(x))
Eq(F_101(x), F_4(x)*F_99(x))
Eq(F_102(x), F_52(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "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, 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": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], 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