0132_0321_1230_1320_2031
Counting sequence:
1, 1, 2, 6, 19, 56, 160, 454, 1288, 3656, 10380, 29472, 83680, 237592, 674592, 1915360, 5438256, 15440768, 43840768, 124476512, 353424512, 1003473536, 2849149120, 8089551360, 22968556032, 65214316928, 185162146304, 525728429568, 1492693766912, 4238185641984, 12033424359424, 34166342403584, 97008043460608, 275433652946944, 782035122752512, 2220421966143488, 6304414679457792, 17900041098762240, 50823349609504768, 144302063401885696, 409714937367048192, 1163298195079659520, 3302937157654216704, 9377985725032325120, 26626790659671752704, 75601094053866143744, 214653185026842214400, 609461945211247788032, 1730437228845354582016, 4913207504590111604736, 13950004993401523666944, 39608064412936357412864, 112458652687319558193152, 319302363084335850455040, 906590970413937883873280, 2574071734693047250059264, 7308527783285109165654016, 20751006135196123430125568, 58918056877030151558004736, 167285258533906330842824704, 474970818897896963999531008, 1348578355210022835742834688, 3829000662316316148658864128, 10871630866220967179663179776, 30867677526038649795502931968, 87642187963903362760676737024, 248841303483900786220021579776, 706531817132066993428385234944, 2006046430520471554354808094720, 5695741060521419816145734598656, 16171842154267927034020476485632, 45916497236026971980208583737344, 130370102448079019417043898204160, 370158105156744043815382210838528, 1050985005306714041553770418012160, 2984047805496038029787640625102848, 8472567411070784040566245250039808, 24056048432912412126221959335772160, 68302019698358588402198137593135104, 193929019883926273185037203529531392, 550620097608095563383800182417129472, 1563368350293394337599448190736662528, 4438851050509047643232666440337195008, 12603170996078804349300473363236388864, 35784016482865815499470124073070100480, 101601084048166139887143935720009236480, 288474612253358906249296193314229321728, 819062145786502696447549278523020541952, 2325552302228907440567300212275183353856, 6602909850276336788977596121637109891072, 18747554483762722786536282194493747232768, 53229683138403358871369344715976916074496, 151134334319115217917287442329206895149056, 429113713690372881756744954841907410763776, 1218376883761837373100568739482755894607872, 3459321348924088401209870023221807725674496, 9822005288029749875950695044640022145794048, 27887489523946320645164437564638369469693952, 79180579641514459879274710126437004746948608, 224816371046332056688342480336474585400606720, 638318144667163028526599955969427061554020352
Generating function in Maple syntax:
-(x^4+2*x^2-3*x+1)/(2*x^3-4*x^2+4*x-1)
Generating function in latex syntax:
-\frac{x^{4}+2 x^{2}-3 x +1}{2 x^{3}-4 x^{2}+4 x -1}
Generating function in sympy syntax:
(-x**4 - 2*x**2 + 3*x - 1)/(2*x**3 - 4*x**2 + 4*x - 1)
Implicit equation for the generating function in Maple syntax:
(2*x^3-4*x^2+4*x-1)*F(x)+x^4+2*x^2-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{3}-4 x^{2}+4 x -1\right) F \! \left(x \right)+x^{4}+2 x^{2}-3 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/8448*(55*2^(2/3)*((I+7/55*11^(1/2))*3^(1/2)+21/55*I*11^(1/2)+1)*(13+3*11^(1/2)*3^(1/2))^(2/3)+5632+352*2^(1/3)*((I+2/11*11^(1/2))*3^(1/2)-6/11*I*11^(1/2)-1)*(13+3*11^(1/2)*3^(1/2))^(1/3))*(13/384*2^(2/3)*((I-3/13*11^(1/2))*3^(1/2)-9/13*I*11^(1/2)+1)*(13+3*11^(1/2)*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(26+6*11^(1/2)*3^(1/2))^(1/3)+1/12*(26+6*11^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/8448*(-352*2^(1/3)*((I-2/11*11^(1/2))*3^(1/2)-6/11*I*11^(1/2)+1)*(13+3*11^(1/2)*3^(1/2))^(1/3)+5632-55*2^(2/3)*((I-7/55*11^(1/2))*3^(1/2)+21/55*I*11^(1/2)-1)*(13+3*11^(1/2)*3^(1/2))^(2/3))*(-13/384*2^(2/3)*((I+3/13*11^(1/2))*3^(1/2)-9/13*I*11^(1/2)-1)*(13+3*11^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(26+6*11^(1/2)*3^(1/2))^(1/3)+1/12*(26+6*11^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)-1/66*(2^(1/3)*(11^(1/2)*3^(1/2)-11/2)*(13+3*11^(1/2)*3^(1/2))^(1/3)-44+(7/64*11^(1/2)*3^(1/2)*2^(2/3)+55/64*2^(2/3))*(13+3*11^(1/2)*3^(1/2))^(2/3))*(1/192*2^(2/3)*(3*11^(1/2)*3^(1/2)-13)*(13+3*11^(1/2)*3^(1/2))^(2/3)-1/6*(26+6*11^(1/2)*3^(1/2))^(1/3)+2/3)^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(55 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{7 \sqrt{11}}{55}\right) \sqrt{3}+\frac{21 \,\mathrm{I} \sqrt{11}}{55}+1\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+5632+352 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{2 \sqrt{11}}{11}\right) \sqrt{3}-\frac{6 \,\mathrm{I} \sqrt{11}}{11}-1\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{13 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{3 \sqrt{11}}{13}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{11}}{13}+1\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}-\frac{\mathrm{I} \sqrt{3}\, \left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{8448}\\+\\\frac{\left(-352 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{2 \sqrt{11}}{11}\right) \sqrt{3}-\frac{6 \,\mathrm{I} \sqrt{11}}{11}+1\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+5632-55 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{7 \sqrt{11}}{55}\right) \sqrt{3}+\frac{21 \,\mathrm{I} \sqrt{11}}{55}-1\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{13 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{3 \sqrt{11}}{13}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{11}}{13}-1\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}+\frac{\mathrm{I} \sqrt{3}\, \left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{8448}\\-\\\frac{\left(2^{\frac{1}{3}} \left(\sqrt{11}\, \sqrt{3}-\frac{11}{2}\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}-44+\left(\frac{7 \sqrt{11}\, \sqrt{3}\, 2^{\frac{2}{3}}}{64}+\frac{55 \,2^{\frac{2}{3}}}{64}\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{2}{3}} \left(3 \sqrt{11}\, \sqrt{3}-13\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{192}-\frac{\left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{2}{3}\right)^{-n}}{66} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+3) = 2*a(n)-4*a(n+1)+4*a(n+2), n >= 5
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(n +3\right) = 2 a \! \left(n \right)-4 a \! \left(n +1\right)+4 a \! \left(n +2\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19482/
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[24,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[12,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[10,x]*F[12,x]
F[23,x] = F[12,x]*F[13,x]
F[24,x] = F[25,x]+F[35,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[16,x]+F[28,x]
F[28,x] = F[25,x]+F[29,x]
F[29,x] = F[18,x]+F[30,x]+F[34,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[12,x]
F[33,x] = F[29,x]
F[34,x] = F[12,x]*F[25,x]
F[35,x] = F[18,x]+F[36,x]+F[70,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[45,x]
F[38,x] = F[39,x]+F[6,x]
F[39,x] = F[18,x]+F[22,x]+F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]+F[43,x]
F[43,x] = F[18,x]+F[22,x]+F[44,x]
F[44,x] = F[12,x]*F[42,x]
F[45,x] = F[35,x]+F[46,x]
F[46,x] = F[18,x]+F[47,x]+F[51,x]+F[68,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[39,x]
F[50,x] = F[46,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[18,x]+F[53,x]+F[66,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[10,x]+F[43,x]
F[56,x] = F[52,x]+F[57,x]
F[57,x] = F[18,x]+F[51,x]+F[58,x]+F[62,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[43,x]
F[61,x] = F[57,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[34,x]
F[65,x] = 2*F[18,x]+F[51,x]+F[62,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[25,x]+F[52,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[63,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[67,x]+F[72,x]
F[72,x] = F[73,x]+F[76,x]
F[73,x] = F[74,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[25,x]+F[64,x]
F[76,x] = 2*F[18,x]+F[77,x]+F[80,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[52,x]+F[79,x]
F[79,x] = F[51,x]
F[80,x] = F[12,x]*F[72,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_{24}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{35}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right)
F_{33}\! \left(x \right) = F_{29}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18}\! \left(x \right)+F_{36}\! \left(x \right)+F_{70}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \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_{18}\! \left(x \right)+F_{22}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{35}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{18}\! \left(x \right)+F_{47}\! \left(x \right)+F_{51}\! \left(x \right)+F_{68}\! \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_{39}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{66}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \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_{10}\! \left(x \right)+F_{43}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right)+F_{51}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \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_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{43}\! \left(x \right)
F_{61}\! \left(x \right) = F_{57}\! \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_{34}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{51}\! \left(x \right)+F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{25}\! \left(x \right)+F_{52}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{76}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{25}\! \left(x \right)+F_{64}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{52}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{51}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \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_24(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_12(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_10(x)*F_12(x))
Eq(F_23(x), F_12(x)*F_13(x))
Eq(F_24(x), F_25(x) + F_35(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_16(x) + F_28(x))
Eq(F_28(x), F_25(x) + F_29(x))
Eq(F_29(x), F_18(x) + F_30(x) + F_34(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_12(x))
Eq(F_33(x), F_29(x))
Eq(F_34(x), F_12(x)*F_25(x))
Eq(F_35(x), F_18(x) + F_36(x) + F_70(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_45(x))
Eq(F_38(x), F_39(x) + F_6(x))
Eq(F_39(x), F_18(x) + F_22(x) + F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x) + F_43(x))
Eq(F_43(x), F_18(x) + F_22(x) + F_44(x))
Eq(F_44(x), F_12(x)*F_42(x))
Eq(F_45(x), F_35(x) + F_46(x))
Eq(F_46(x), F_18(x) + F_47(x) + F_51(x) + F_68(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_39(x))
Eq(F_50(x), F_46(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_18(x) + F_53(x) + F_66(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_10(x) + F_43(x))
Eq(F_56(x), F_52(x) + F_57(x))
Eq(F_57(x), F_18(x) + F_51(x) + F_58(x) + F_62(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_43(x))
Eq(F_61(x), F_57(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_34(x))
Eq(F_65(x), 2*F_18(x) + F_51(x) + F_62(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_25(x) + F_52(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_63(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_67(x) + F_72(x))
Eq(F_72(x), F_73(x) + F_76(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_25(x) + F_64(x))
Eq(F_76(x), 2*F_18(x) + F_77(x) + F_80(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_52(x) + F_79(x))
Eq(F_79(x), F_51(x))
Eq(F_80(x), F_12(x)*F_72(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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