0213_0321_1320_2103
Counting sequence:
1, 1, 2, 6, 20, 64, 189, 520, 1362, 3463, 8665, 21511, 53207, 131388, 324193, 799621, 1971878, 4862210, 11988568, 29559144, 72880689, 179693100, 443046786, 1092364151, 2693302457, 6640529959, 16372700579, 40368060516, 99530329721, 245399118769, 605049008802, 1491791431366, 3678118038660, 9068662025176, 22359432202525, 55128772801288, 135923916269210, 335130097679199, 826287127775905, 2037269771516623, 5023033740226007, 12384647486650148, 30535230560022025, 75286786027517061, 185624933769910326, 457671496622123922, 1128421675721497176, 2782204021085102096, 6859722195599296385, 16913133704136168796, 41700535901803501850, 102815641673331054975, 253499288296715219537, 625020552525616111423, 1541032693638881515635, 3799525876817591166844, 9368001696652805426385, 23097475483439910421249, 56948471080948388056738, 140410511996552416403110, 346192119031787456595860, 853561329387232908541584, 2104516258379651600399965, 5188834743677804228683240, 12793441670974657638361730, 31543141740648564211234583, 77771862838754381339183497, 191752067664698677215650487, 472778381686968494800392567, 1165668776940643737140872812, 2874039402321828506208484497, 7086148869645000823530756389, 17471404797792791974503226406, 43076993049911649298984582210, 106209394819617639794014471160, 261866828422290688604644658136, 645651318740809503345460028849, 1591899317310637489740660243820, 3924941160805374508049274811218, 9677222012890739093530178118247, 23859880199467996303096319154441, 58828234215834413268882210466423, 145045201904669888840637780454627, 357619277137911477927429026956276, 881735801675799707313173836957961, 2173982426727651106137463554421233, 5360108529945340321766272113771010, 13215729391170504878317292193858982, 32584322195138271222850198869851972, 80338967414536581465113150851433576, 198081446855966484381153485638059133, 488383916936597843867598784904632488, 1204145335710168697959967163982543114, 2968906098725585025645335188321195695, 7320049467161290144384301288085973137, 18048103382147741543190430702685552063, 44498884488961270527776221935275938487, 109715169446590244828305638091933922068, 270510565487997851303912734799412661241, 666963068185923992657451414543808859493, 1644444953643477448595158898453973907574
Generating function in Maple syntax:
-(4*x^5-15*x^4+19*x^3-15*x^2+6*x-1)/(3*x^3-5*x^2+4*x-1)/(x-1)^3
Generating function in latex syntax:
-\frac{4 x^{5}-15 x^{4}+19 x^{3}-15 x^{2}+6 x -1}{\left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-4*x**5 + 15*x**4 - 19*x**3 + 15*x**2 - 6*x + 1)/((x - 1)**3*(3*x**3 - 5*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
(3*x^3-5*x^2+4*x-1)*(x-1)^3*F(x)+4*x^5-15*x^4+19*x^3-15*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+4 x^{5}-15 x^{4}+19 x^{3}-15 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
1/45012*(-1705*2^(2/3)*((-15/31*I+5/31*3^(1/2))*31^(1/2)+I*3^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(1/3)-15004-620*((3/62*I+1/62*3^(1/2))*31^(1/2)+I*3^(1/2)+1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3))*(47/8712*((I-9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)+1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/45012*(1705*((-15/31*I-5/31*3^(1/2))*31^(1/2)+I*3^(1/2)+1)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3)-15004+620*2^(1/3)*((3/62*I-1/62*3^(1/2))*31^(1/2)+I*3^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(2/3))*(-47/8712*2^(1/3)*((I+9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(2/3)+1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/45012*((550*2^(2/3)*31^(1/2)*3^(1/2)-3410*2^(2/3))*(47+9*31^(1/2)*3^(1/2))^(1/3)-15004+(20*31^(1/2)*3^(1/2)*2^(1/3)+1240*2^(1/3))*(47+9*31^(1/2)*3^(1/2))^(2/3))*(1/4356*2^(1/3)*(9*31^(1/2)*3^(1/2)-47)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/18*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)-n^2-2*n+2
Explicit closed form in latex syntax:
\frac{\left(-1705 \,2^{\frac{2}{3}} \left(\left(-\frac{15 \,\mathrm{I}}{31}+\frac{5 \sqrt{3}}{31}\right) \sqrt{31}+\mathrm{I} \sqrt{3}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-15004-620 \left(\left(\frac{3 \,\mathrm{I}}{62}+\frac{\sqrt{3}}{62}\right) \sqrt{31}+\mathrm{I} \sqrt{3}+1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{47 \left(\left(\mathrm{I}-\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}+1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}-\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{45012}+\frac{\left(1705 \left(\left(-\frac{15 \,\mathrm{I}}{31}-\frac{5 \sqrt{3}}{31}\right) \sqrt{31}+\mathrm{I} \sqrt{3}+1\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-15004+620 \,2^{\frac{1}{3}} \left(\left(\frac{3 \,\mathrm{I}}{62}-\frac{\sqrt{3}}{62}\right) \sqrt{31}+\mathrm{I} \sqrt{3}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{47 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}+\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{45012}+\frac{\left(\left(550 \,2^{\frac{2}{3}} \sqrt{31}\, \sqrt{3}-3410 \,2^{\frac{2}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-15004+\left(20 \sqrt{31}\, \sqrt{3}\, 2^{\frac{1}{3}}+1240 \,2^{\frac{1}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(9 \sqrt{31}\, \sqrt{3}-47\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{4356}-\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{18}+\frac{5}{9}\right)^{-n}}{45012}-n^{2}-2 n +2
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(n+3) = 3*a(n)-5*a(n+1)+4*a(n+2)+n*(n+2), n >= 6
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(n +3\right) = 3 a \! \left(n \right)-5 a \! \left(n +1\right)+4 a \! \left(n +2\right)+n \left(n +2\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15747/
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[17,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[6,x]
F[10,x] = F[11,x]+F[14,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[64,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[39,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[19,x]+F[24,x]+F[30,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[22,x]+F[26,x]
F[26,x] = F[14,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[26,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[10,x]+F[32,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[11,x]+F[33,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[32,x]
F[39,x] = F[40,x]+F[44,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[2,x]+F[40,x]
F[44,x] = 2*F[19,x]+F[45,x]+F[62,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[39,x]+F[47,x]
F[47,x] = F[48,x]+F[59,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[48,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[11,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[55,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[47,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[51,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[17,x]+F[66,x]
F[66,x] = F[52,x]+F[67,x]
F[67,x] = 2*F[19,x]+F[68,x]+F[76,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[14,x]+F[71,x]
F[71,x] = 2*F[19,x]+F[72,x]+F[74,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[70,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[32,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[66,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_{17}\! \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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \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_{10}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{64}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{39}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right)+F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{32}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \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_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{40}\! \left(x \right)
F_{44}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{45}\! \left(x \right)+F_{62}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{39}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{59}\! \left(x \right)
F_{48}\! \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_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \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_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \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_{55}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{17}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{52}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{68}\! \left(x \right)+F_{76}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{14}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{70}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{32}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{66}\! \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_17(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_6(x))
Eq(F_10(x), F_11(x) + F_14(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_11(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_64(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_39(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_19(x) + F_24(x) + F_30(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_22(x) + F_26(x))
Eq(F_26(x), F_14(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_26(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_10(x) + F_32(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_11(x) + F_33(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_32(x))
Eq(F_39(x), F_40(x) + F_44(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_2(x) + F_40(x))
Eq(F_44(x), 2*F_19(x) + F_45(x) + F_62(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_39(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_59(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_48(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_11(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_55(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_47(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_51(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_17(x) + F_66(x))
Eq(F_66(x), F_52(x) + F_67(x))
Eq(F_67(x), 2*F_19(x) + F_68(x) + F_76(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_14(x) + F_71(x))
Eq(F_71(x), 2*F_19(x) + F_72(x) + F_74(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_70(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_32(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_66(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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