0132_1203_1320_3120
Counting sequence:
1, 1, 2, 6, 20, 64, 190, 527, 1386, 3502, 8586, 20573, 48422, 112356, 257686, 585275, 1318354, 2948442, 6552786, 14482489, 31849358, 69728976, 152041982, 330299671, 715126810, 1543501574, 3321886170, 7130313877, 15267263286, 32614904252, 69524779046, 147907931763, 314069478562, 665719925426, 1408749267106, 2976412329585, 6279242179614, 13228499263912, 27831388069646, 58480274693199, 122732985440618, 257285720888926, 538760697598762, 1126999418458061, 2355153906682950, 4917015999400084, 10256244463879350, 21374506043949227, 44508230692355186, 92605267337787402, 192528884070069106, 399975941905821353, 830351181296413102, 1722626857469191296, 3571354504504778526, 7399414187769698695, 15321245932314399674, 31705341376688262582, 65572410574514390906, 135540334385342415109, 280015810431387925078, 578190134560333722476, 1193273757268086582342, 2461487412335618254051, 5075160463279340346690, 10459303889793315722594, 21545797078092756241730, 44364419497271471588577, 91311383164862280449086, 187861641646658073604952, 386348607879772848990766, 794243012837638454321343, 1632167915641821126924042, 3352880202837448101661966, 6885210332023942721503946, 14134042883228848124524605, 29004774937785360902450534, 59501817684157529692496452, 122025949917351632321828566, 250172086796502324840680219, 512735663244054598722174738, 1050556537245112752819581626, 2151887958914039930976904722, 4406534612495323341803919641, 9021004465964362901657390030, 18462715117154616756112621104, 37776514011317932451218485310, 77274538389767096847218663927, 158030783140024325717591216986, 323102350253484251748671308902, 660441010958750376658682656026, 1349664127830885844708770063733, 2757511437508184562337799083382, 5632627178748480250791015089436, 11502938845039753514362662155366, 23486198425322234575386184639315, 47942941841444207286293282804194, 97846780705116456928026778517522, 199654969535946130735730754694626, 407311983485832959568409448520529, 830786512124575844005901863061598
Generating function in Maple syntax:
-(x^7+14*x^6-49*x^5+77*x^4-68*x^3+34*x^2-9*x+1)/(2*x-1)^3/(x-1)^4
Generating function in latex syntax:
-\frac{x^{7}+14 x^{6}-49 x^{5}+77 x^{4}-68 x^{3}+34 x^{2}-9 x +1}{\left(2 x -1\right)^{3} \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-x**7 - 14*x**6 + 49*x**5 - 77*x**4 + 68*x**3 - 34*x**2 + 9*x - 1)/((x - 1)**4*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^3*(x-1)^4*F(x)+x^7+14*x^6-49*x^5+77*x^4-68*x^3+34*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{3} \left(x -1\right)^{4} F \! \left(x \right)+x^{7}+14 x^{6}-49 x^{5}+77 x^{4}-68 x^{3}+34 x^{2}-9 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/48*(3*n^2+15*n-42)*2^n-1/6*n^3+1/2*n^2-1/3*n+2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(3 n^{2}+15 n -42\right) 2^{n}}{48}-\frac{n^{3}}{6}+\frac{n^{2}}{2}-\frac{n}{3}+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) = 20
a(5) = 64
a(6) = 190
a(7) = 527
a(n+3) = 8*a(n)-12*a(n+1)+6*a(n+2)+1/6*(n-1)*(n-2)*(n-9), n >= 8
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) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 190
a \! \left(7\right) = 527
a \! \left(n +3\right) = 8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)+\frac{\left(n -1\right) \left(n -2\right) \left(n -9\right)}{6}, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15569/
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[12,x]*F[4,x]
F[4,x] = F[29,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[23,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[9,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[10,x]
F[22,x] = F[18,x]
F[23,x] = F[24,x]+F[25,x]+F[28,x]
F[24,x] = 0
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[21,x]+F[27,x]
F[27,x] = F[23,x]
F[28,x] = F[12,x]*F[13,x]
F[29,x] = F[14,x]+F[30,x]
F[30,x] = F[24,x]+F[31,x]+F[80,x]
F[31,x] = F[12,x]*F[32,x]
F[32,x] = F[33,x]+F[52,x]
F[33,x] = F[34,x]+F[6,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[10,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[37,x]
F[40,x] = F[41,x]+F[46,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[10,x]
F[45,x] = F[41,x]
F[46,x] = 2*F[24,x]+F[47,x]+F[51,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[38,x]
F[50,x] = F[46,x]
F[51,x] = F[12,x]*F[40,x]
F[52,x] = F[30,x]+F[53,x]
F[53,x] = 2*F[24,x]+F[54,x]+F[58,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[34,x]
F[57,x] = F[53,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[60,x]+F[67,x]
F[60,x] = F[18,x]+F[61,x]
F[61,x] = 2*F[24,x]+F[62,x]+F[66,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[38,x]
F[65,x] = F[61,x]
F[66,x] = F[12,x]*F[60,x]
F[67,x] = F[68,x]+F[73,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[18,x]
F[72,x] = F[68,x]
F[73,x] = 2*F[24,x]+F[74,x]+F[75,x]+F[79,x]
F[74,x] = 0
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[61,x]
F[78,x] = F[73,x]
F[79,x] = F[12,x]*F[67,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[89,x]
F[82,x] = F[14,x]+F[83,x]
F[83,x] = F[24,x]+F[84,x]+F[88,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[10,x]+F[38,x]
F[87,x] = F[61,x]+F[83,x]
F[88,x] = F[12,x]*F[82,x]
F[89,x] = F[90,x]+F[98,x]
F[90,x] = F[19,x]+F[24,x]+F[91,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[17,x]+F[93,x]
F[93,x] = F[90,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[12,x]*F[96,x]
F[96,x] = F[22,x]+F[97,x]
F[97,x] = F[94,x]
F[98,x] = F[103,x]+F[24,x]+F[62,x]+F[99,x]
F[99,x] = F[100,x]*F[12,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[83,x]
F[102,x] = F[98,x]
F[103,x] = F[12,x]*F[89,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{29}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{23}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{10}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \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_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{29}\! \left(x \right) = F_{14}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)+F_{80}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{52}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{6}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{10}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{46}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{38}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{52}\! \left(x \right) = F_{30}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{54}\! \left(x \right)+F_{58}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{34}\! \left(x \right)
F_{57}\! \left(x \right) = F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{67}\! \left(x \right)
F_{60}\! \left(x \right) = F_{18}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{38}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{73}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{18}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{74}\! \left(x \right)+F_{75}\! \left(x \right)+F_{79}\! \left(x \right)
F_{74}\! \left(x \right) = 0
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{61}\! \left(x \right)
F_{78}\! \left(x \right) = F_{73}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{89}\! \left(x \right)
F_{82}\! \left(x \right) = F_{14}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{24}\! \left(x \right)+F_{84}\! \left(x \right)+F_{88}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{10}\! \left(x \right)+F_{38}\! \left(x \right)
F_{87}\! \left(x \right) = F_{61}\! \left(x \right)+F_{83}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{98}\! \left(x \right)
F_{90}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{17}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{90}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{22}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{94}\! \left(x \right)
F_{98}\! \left(x \right) = F_{103}\! \left(x \right)+F_{24}\! \left(x \right)+F_{62}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{83}\! \left(x \right)
F_{102}\! \left(x \right) = F_{98}\! \left(x \right)
F_{103}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_29(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_23(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_9(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_10(x))
Eq(F_22(x), F_18(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_28(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_21(x) + F_27(x))
Eq(F_27(x), F_23(x))
Eq(F_28(x), F_12(x)*F_13(x))
Eq(F_29(x), F_14(x) + F_30(x))
Eq(F_30(x), F_24(x) + F_31(x) + F_80(x))
Eq(F_31(x), F_12(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_52(x))
Eq(F_33(x), F_34(x) + F_6(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_10(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_37(x))
Eq(F_40(x), F_41(x) + F_46(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_10(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), 2*F_24(x) + F_47(x) + F_51(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_38(x))
Eq(F_50(x), F_46(x))
Eq(F_51(x), F_12(x)*F_40(x))
Eq(F_52(x), F_30(x) + F_53(x))
Eq(F_53(x), 2*F_24(x) + F_54(x) + F_58(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_34(x))
Eq(F_57(x), F_53(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_67(x))
Eq(F_60(x), F_18(x) + F_61(x))
Eq(F_61(x), 2*F_24(x) + F_62(x) + F_66(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_38(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_12(x)*F_60(x))
Eq(F_67(x), F_68(x) + F_73(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_18(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), 2*F_24(x) + F_74(x) + F_75(x) + F_79(x))
Eq(F_74(x), 0)
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_61(x))
Eq(F_78(x), F_73(x))
Eq(F_79(x), F_12(x)*F_67(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_89(x))
Eq(F_82(x), F_14(x) + F_83(x))
Eq(F_83(x), F_24(x) + F_84(x) + F_88(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_10(x) + F_38(x))
Eq(F_87(x), F_61(x) + F_83(x))
Eq(F_88(x), F_12(x)*F_82(x))
Eq(F_89(x), F_90(x) + F_98(x))
Eq(F_90(x), F_19(x) + F_24(x) + F_91(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_17(x) + F_93(x))
Eq(F_93(x), F_90(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_12(x)*F_96(x))
Eq(F_96(x), F_22(x) + F_97(x))
Eq(F_97(x), F_94(x))
Eq(F_98(x), F_103(x) + F_24(x) + F_62(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_12(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_83(x))
Eq(F_102(x), F_98(x))
Eq(F_103(x), F_12(x)*F_89(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": [1, 2, 0, 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, 1, 2, 0], "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": [1, 2, 0, 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, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": 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{"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 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], "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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": 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{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"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], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 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