0132_0321_1023_1302_3021
Counting sequence:
1, 1, 2, 6, 19, 52, 138, 364, 957, 2511, 6581, 17238, 45140, 118190, 309439, 810137, 2120983, 5552824, 14537502, 38059696, 99641601, 260865123, 682953785, 1787996250, 4681034984, 12255108722, 32084291203, 83997764909, 219909003547, 575729245756, 1507278733746, 3946106955508, 10331042132805, 27047019442935, 70810016196029, 185383029145182, 485339071239548, 1270634184573494, 3326563482480967, 8709056262869441, 22800605306127391, 59692759655512768, 156277673660410950, 409140261325720120, 1071143110316749449, 2804289069624528267, 7341724098556835393, 19220883226045977954, 50320925579581098512, 131741893512697317626, 344904754958510854411, 902972371362835245653, 2364012359129994882595, 6189064706027149402180, 16203181758951453323994, 42420480570827210569852, 111058259953530178385613, 290754299289763324587039, 761204637915759795375557, 1992859614457516061539686, 5217374205456788389243556, 13659263001912849106191038, 35760414800281758929329615, 93621981398932427681797865, 245105529396515524116064039, 641694606790614144666394312, 1679978290975326909883118958, 4398240266135366584982962624, 11514742507430772845065768977, 30145987256156951950214344371, 78923219261040083005577264201, 206623670526963297066517448298, 540947792319849808193975080760, 1416219706432586127515407794050, 3707711326977908574352248301459, 9706914274501139595541337110397, 25413031496525510212271763029803, 66532180215075391041273951979084, 174183509148700662911550092907522, 456018347231026597693376326743556, 1193871532544379130168578887323221, 3125596250402110792812360335226183, 8182917218661953248268502118355405, 21423155405583748951993146019840110, 56086548998089293607710935941165004, 146836491588684131871139661803654982, 384422925767963102005708049469800023, 1006432285715205174145984486605745169, 2634873931377652420432245410347435567, 6898189508417752087150751744436561616, 18059694593875603841020009822962249366, 47280894273209059435909277724450186568, 123782988225751574466707823350388310425, 324068070404045663964214192326714744795, 848421222986385417425934753629755924049, 2221195598555110588313590068562553027442, 5815165572678946347514835452057903158368, 15224301119481728454230916287611156447754, 39857737785766239015177913410775566184987, 104348912237816988591302823944715542107301, 273188998927684726758730558423371060137011
Generating function in Maple syntax:
(x^7+2*x^6-4*x^5+x^4-x^3+5*x^2-4*x+1)/(x^2-3*x+1)/(x-1)^2
Generating function in latex syntax:
\frac{x^{7}+2 x^{6}-4 x^{5}+x^{4}-x^{3}+5 x^{2}-4 x +1}{\left(x^{2}-3 x +1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(x**7 + 2*x**6 - 4*x**5 + x**4 - x**3 + 5*x**2 - 4*x + 1)/((x - 1)**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(x-1)^2*F(x)+x^7+2*x^6-4*x^5+x^4-x^3+5*x^2-4*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(x -1\right)^{2} F \! \left(x \right)+x^{7}+2 x^{6}-4 x^{5}+x^{4}-x^{3}+5 x^{2}-4 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,65,n = 1,23,n = 2,7,n = 3,1,0)-n+4-77/5*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)+77/5*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)-34*(3/2+1/2*5^(1/2))^(-n)-34*(3/2-1/2*5^(1/2))^(-n)
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}65 & n =0 \\ 23 & n =1 \\ 7 & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)-n +4-\frac{77 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}+\frac{77 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}-34 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}-34 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 52
a(6) = 138
a(7) = 364
a(n+2) = -a(n)+3*a(n+1)-3+n, 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) = 19
a \! \left(5\right) = 52
a \! \left(6\right) = 138
a \! \left(7\right) = 364
a \! \left(n +2\right) = -a \! \left(n \right)+3 a \! \left(n +1\right)-3+n, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19325/
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[20,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[11,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[19,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[4,x]
F[18,x] = F[16,x]
F[19,x] = F[13,x]*F[4,x]
F[20,x] = F[21,x]+F[34,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[10,x]+F[24,x]
F[24,x] = F[21,x]+F[25,x]
F[25,x] = F[15,x]+F[26,x]+F[33,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[17,x]+F[28,x]
F[28,x] = F[29,x]+F[31,x]
F[29,x] = F[15,x]+F[26,x]+F[30,x]
F[30,x] = F[21,x]*F[4,x]
F[31,x] = F[32,x]
F[32,x] = F[28,x]*F[4,x]
F[33,x] = F[24,x]*F[4,x]
F[34,x] = F[15,x]+F[35,x]+F[83,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[44,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[1,x]+F[4,x]
F[41,x] = F[15,x]+F[16,x]+F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[11,x]
F[44,x] = F[45,x]+F[49,x]
F[45,x] = F[15,x]+F[35,x]+F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[21,x]+F[48,x]
F[48,x] = F[30,x]
F[49,x] = F[15,x]+F[50,x]+F[59,x]+F[81,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[55,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[4,x]
F[55,x] = F[56,x]
F[56,x] = 2*F[15,x]+F[50,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[48,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[80,x]
F[61,x] = F[15,x]+F[30,x]+F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[4,x]+F[65,x]
F[65,x] = F[15,x]+F[16,x]+F[66,x]
F[66,x] = F[11,x]*F[4,x]
F[67,x] = F[61,x]+F[68,x]
F[68,x] = F[15,x]+F[59,x]+F[69,x]+F[76,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[73,x]
F[71,x] = F[72,x]
F[72,x] = x^2
F[73,x] = F[74,x]
F[74,x] = 2*F[15,x]+F[69,x]+F[75,x]
F[75,x] = F[4,x]*F[48,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[21,x]+F[77,x]
F[80,x] = F[59,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[77,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[21,x]+F[86,x]
F[86,x] = F[15,x]+F[62,x]+F[87,x]
F[87,x] = F[4,x]*F[85,x]
F[88,x] = F[77,x]+F[89,x]
F[89,x] = 2*F[15,x]+F[90,x]+F[93,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[61,x]+F[92,x]
F[92,x] = F[90,x]
F[93,x] = F[4,x]*F[88,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_{20}\! \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_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{34}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{10}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{17}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{31}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{15}\! \left(x \right)+F_{35}\! \left(x \right)+F_{83}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{11}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{49}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right)+F_{35}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{21}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{30}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right)+F_{50}\! \left(x \right)+F_{59}\! \left(x \right)+F_{81}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{55}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{48}\! \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_{80}\! \left(x \right)
F_{61}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right)+F_{59}\! \left(x \right)+F_{69}\! \left(x \right)+F_{76}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{73}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = x^{2}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{21}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{59}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{77}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{21}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right)+F_{62}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{77}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{61}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \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_20(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_11(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_19(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_4(x))
Eq(F_18(x), F_16(x))
Eq(F_19(x), F_13(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_34(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_10(x) + F_24(x))
Eq(F_24(x), F_21(x) + F_25(x))
Eq(F_25(x), F_15(x) + F_26(x) + F_33(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_17(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_31(x))
Eq(F_29(x), F_15(x) + F_26(x) + F_30(x))
Eq(F_30(x), F_21(x)*F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_28(x)*F_4(x))
Eq(F_33(x), F_24(x)*F_4(x))
Eq(F_34(x), F_15(x) + F_35(x) + F_83(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_44(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_1(x) + F_4(x))
Eq(F_41(x), F_15(x) + F_16(x) + F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_11(x))
Eq(F_44(x), F_45(x) + F_49(x))
Eq(F_45(x), F_15(x) + F_35(x) + F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_21(x) + F_48(x))
Eq(F_48(x), F_30(x))
Eq(F_49(x), F_15(x) + F_50(x) + F_59(x) + F_81(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_55(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_4(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), 2*F_15(x) + F_50(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_48(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_80(x))
Eq(F_61(x), F_15(x) + F_30(x) + F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_4(x) + F_65(x))
Eq(F_65(x), F_15(x) + F_16(x) + F_66(x))
Eq(F_66(x), F_11(x)*F_4(x))
Eq(F_67(x), F_61(x) + F_68(x))
Eq(F_68(x), F_15(x) + F_59(x) + F_69(x) + F_76(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_73(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), x**2)
Eq(F_73(x), F_74(x))
Eq(F_74(x), 2*F_15(x) + F_69(x) + F_75(x))
Eq(F_75(x), F_4(x)*F_48(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_21(x) + F_77(x))
Eq(F_80(x), F_59(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_77(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_21(x) + F_86(x))
Eq(F_86(x), F_15(x) + F_62(x) + F_87(x))
Eq(F_87(x), F_4(x)*F_85(x))
Eq(F_88(x), F_77(x) + F_89(x))
Eq(F_89(x), 2*F_15(x) + F_90(x) + F_93(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_61(x) + F_92(x))
Eq(F_92(x), F_90(x))
Eq(F_93(x), F_4(x)*F_88(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:
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[[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": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"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, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": 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