0132_0213_0231_3120_3201
Counting sequence:
1, 1, 2, 6, 19, 51, 111, 212, 375, 637, 1067, 1798, 3091, 5463, 9943, 18584, 35487, 68849, 135059, 266890, 529883, 1055115, 2104735, 4203036, 8398599, 16788581, 33567291, 67123342, 134233955, 268453567, 536891047, 1073764128, 2147508271, 4294994393, 8589964323, 17179901714, 34359773867, 68719515379, 137438995439, 274877952420, 549755863063, 1099511680845, 2199023312715, 4398046572566, 8796093088179, 17592186115111, 35184372164471, 70368744258472, 140737488441535, 281474976802497, 562949953519027, 1125899906946458, 2251799813795451, 4503599627487323, 9007199254864703, 18014398509612844, 36028797019102247, 72057594038073909, 144115188076009819, 288230376151873950, 576460752303594243, 1152921504607026575, 2305843009213882695, 4611686018427586096, 9223372036854983759, 18446744073709769641, 36893488147419331651, 73786976294838445602, 147573952589676663115, 295147905179353087427, 590295810358705925007, 1180591620717411588788, 2361183241434822904631, 4722366482869645524253, 9444732965739290751083, 18889465931478581191974, 37778931862957162060627, 75557863725914323784439, 151115727451828647218199, 302231454903657294071480, 604462909807314587763423, 1208925819614629175132305, 2417851639229258349854675, 4835703278458516699283626, 9671406556917033398125339, 19342813113834066795792171, 38685626227668133591108831, 77371252455336267181724732, 154742504910672534362938695, 309485009821345068725348357, 618970019642690137450148987, 1237940039285380274899731118, 2475880078570760549798875811, 4951760157141521099597145183, 9903520314283042199193663463, 19807040628566084398386679104, 39614081257132168796772689007, 79228162514264337593544686969, 158456325028528675187088660579, 316912650057057350374176585010, 633825300114114700748352410603
Generating function in Maple syntax:
-(6*x^7-9*x^6-4*x^5+4*x^4-8*x^3+10*x^2-5*x+1)/(2*x-1)/(x-1)^4
Generating function in latex syntax:
-\frac{6 x^{7}-9 x^{6}-4 x^{5}+4 x^{4}-8 x^{3}+10 x^{2}-5 x +1}{\left(2 x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-6*x**7 + 9*x**6 + 4*x**5 - 4*x**4 + 8*x**3 - 10*x**2 + 5*x - 1)/((x - 1)**4*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x-1)^4*F(x)+6*x^7-9*x^6-4*x^5+4*x^4-8*x^3+10*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x -1\right)^{4} F \! \left(x \right)+6 x^{7}-9 x^{6}-4 x^{5}+4 x^{4}-8 x^{3}+10 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,15+5/6*n^3-5/2*n^2-13/3*n+2^(-1+n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 15+\frac{5 n^{3}}{6}-\frac{5 n^{2}}{2}-\frac{13 n}{3}+2^{-1+n} & \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(5) = 51
a(6) = 111
a(7) = 212
a(n+1) = -5/6*n^3+5*n^2+2*a(n)+11/6*n-21, 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) = 51
a \! \left(6\right) = 111
a \! \left(7\right) = 212
a \! \left(n +1\right) = -\frac{5 n^{3}}{6}+5 n^{2}+2 a \! \left(n \right)+\frac{11 n}{6}-21, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18230/
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[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[22,x]+F[30,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[1,x]+F[14,x]
F[26,x] = F[18,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[14,x]+F[27,x]
F[30,x] = F[31,x]+F[32,x]+F[81,x]
F[31,x] = 0
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[51,x]
F[34,x] = F[35,x]+F[7,x]
F[35,x] = F[31,x]+F[36,x]+F[41,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]
F[38,x] = F[11,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[38,x]*F[4,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[13,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[31,x]+F[36,x]+F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[17,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[18,x]+F[48,x]
F[51,x] = F[52,x]+F[71,x]
F[52,x] = F[31,x]+F[53,x]+F[55,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[52,x]+F[7,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[62,x]
F[57,x] = F[18,x]+F[58,x]
F[58,x] = F[31,x]+F[59,x]+F[61,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[11,x]+F[58,x]
F[61,x] = F[4,x]*F[57,x]
F[62,x] = F[63,x]
F[63,x] = F[28,x]+F[31,x]+F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[70,x]
F[66,x] = F[18,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[11,x]+F[67,x]
F[70,x] = F[48,x]
F[71,x] = 2*F[31,x]+F[72,x]+F[74,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[35,x]+F[71,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[27,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[44,x]+F[80,x]
F[80,x] = F[78,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[96,x]
F[83,x] = F[22,x]+F[84,x]
F[84,x] = F[31,x]+F[85,x]+F[95,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[90,x]
F[87,x] = F[11,x]+F[88,x]
F[88,x] = F[31,x]+F[36,x]+F[89,x]
F[89,x] = F[13,x]*F[4,x]
F[90,x] = F[58,x]+F[91,x]
F[91,x] = 2*F[31,x]+F[92,x]+F[94,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[88,x]+F[91,x]
F[94,x] = F[4,x]*F[76,x]
F[95,x] = F[4,x]*F[83,x]
F[96,x] = F[97,x]
F[97,x] = F[31,x]+F[64,x]+F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[14,x]+F[44,x]
F[101,x] = F[27,x]+F[80,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_{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_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{30}\! \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_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{26}\! \left(x \right) = F_{18}\! \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_{14}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{81}\! \left(x \right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{51}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{7}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)+F_{36}\! \left(x \right)+F_{41}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{31}\! \left(x \right)+F_{36}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{17}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \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_{18}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{71}\! \left(x \right)
F_{52}\! \left(x \right) = F_{31}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{52}\! \left(x \right)+F_{7}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{62}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{31}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{18}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{11}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{48}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{31}\! \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_{35}\! \left(x \right)+F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{27}\! \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_{44}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{96}\! \left(x \right)
F_{83}\! \left(x \right) = F_{22}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{31}\! \left(x \right)+F_{85}\! \left(x \right)+F_{95}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{90}\! \left(x \right)
F_{87}\! \left(x \right) = F_{11}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{31}\! \left(x \right)+F_{36}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{90}\! \left(x \right) = F_{58}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{92}\! \left(x \right)+F_{94}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{31}\! \left(x \right)+F_{64}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{14}\! \left(x \right)+F_{44}\! \left(x \right)
F_{101}\! \left(x \right) = F_{27}\! \left(x \right)+F_{80}\! \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))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_22(x) + F_30(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_1(x) + F_14(x))
Eq(F_26(x), F_18(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_14(x) + F_27(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_81(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_51(x))
Eq(F_34(x), F_35(x) + F_7(x))
Eq(F_35(x), F_31(x) + F_36(x) + F_41(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_11(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_38(x)*F_4(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_13(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_31(x) + F_36(x) + F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_17(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_18(x) + F_48(x))
Eq(F_51(x), F_52(x) + F_71(x))
Eq(F_52(x), F_31(x) + F_53(x) + F_55(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_52(x) + F_7(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_62(x))
Eq(F_57(x), F_18(x) + F_58(x))
Eq(F_58(x), F_31(x) + F_59(x) + F_61(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_11(x) + F_58(x))
Eq(F_61(x), F_4(x)*F_57(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_28(x) + F_31(x) + F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_70(x))
Eq(F_66(x), F_18(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_11(x) + F_67(x))
Eq(F_70(x), F_48(x))
Eq(F_71(x), 2*F_31(x) + F_72(x) + F_74(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_35(x) + F_71(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_27(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_44(x) + F_80(x))
Eq(F_80(x), F_78(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_96(x))
Eq(F_83(x), F_22(x) + F_84(x))
Eq(F_84(x), F_31(x) + F_85(x) + F_95(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_90(x))
Eq(F_87(x), F_11(x) + F_88(x))
Eq(F_88(x), F_31(x) + F_36(x) + F_89(x))
Eq(F_89(x), F_13(x)*F_4(x))
Eq(F_90(x), F_58(x) + F_91(x))
Eq(F_91(x), 2*F_31(x) + F_92(x) + F_94(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_88(x) + F_91(x))
Eq(F_94(x), F_4(x)*F_76(x))
Eq(F_95(x), F_4(x)*F_83(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_31(x) + F_64(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_14(x) + F_44(x))
Eq(F_101(x), F_27(x) + F_80(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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 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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": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [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, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": 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