0132_1032_1230_3120
Counting sequence:
1, 1, 2, 6, 20, 61, 169, 438, 1086, 2613, 6155, 14272, 32692, 74151, 166809, 372618, 827258, 1826665, 4013911, 8781636, 19136304, 41549595, 89915141, 193986286, 417332950, 895483581, 1916796579, 4093640328, 8724151916, 18555600463, 39392902705, 83483426322, 176630529522, 373125283281, 787052756399, 1657857375628, 3487513443688, 7327214206275, 15375982918941, 32229434588406, 67482526153934, 141149805214885, 294943994150011, 615726511553616, 1284229581241380, 2676211302005751, 5572324929567689, 11593250603269018, 24101294880848746, 50067361482406713, 103934635150408455, 215609832160361172, 446982263016520352, 926052673378056811, 1917407541352987189, 3967671271713405438, 8205558521069042118, 16960556196677286285, 35038005100942457171, 72345824414079645976, 149303334846586681564, 307974156918103996575, 634971518662220970081, 1308565907728771315746, 2695530477770808227810, 5550164123177361340321, 11423146267644639835999, 23501151949905968756508, 48330469473119025231576, 99354163580999645001363, 204168563407817317283405, 419405173259860365538822, 861241587313351545845182, 1767935952024323426874741, 3627958050464604935419179, 7442449577002560856782048, 15262688472634693330662548, 31290400315494269185946695, 64129736837369782001988601, 131395125019365008425874346, 269137110591706820018959194, 551119058016819075019174665, 1128230021155352677294535351, 2309048315463941723688792676, 4724482103053970814751732240, 9664153001999345622601167291, 19763519299059957748096561509, 40407136594799365535379222798, 82593811996071465215925940406, 168785387231316066855777464413, 344843672193433742826587287555, 704387882353381376417601679272, 1438486325649611879432782344012, 2937012743204564702198172217071, 5995343610259096671336458612369, 12235799348296698637102943825458, 24966774712307549384165537344978, 50933804976357686030449567067505, 103887928096829112669534504873231, 211856106563142838725136523193516, 431951942027769168560001617226824
Generating function in Maple syntax:
-(2*x^8-2*x^7-6*x^6+17*x^5-35*x^4+42*x^3-26*x^2+8*x-1)/(2*x-1)^3/(x-1)^3
Generating function in latex syntax:
-\frac{2 x^{8}-2 x^{7}-6 x^{6}+17 x^{5}-35 x^{4}+42 x^{3}-26 x^{2}+8 x -1}{\left(2 x -1\right)^{3} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-2*x**8 + 2*x**7 + 6*x**6 - 17*x**5 + 35*x**4 - 42*x**3 + 26*x**2 - 8*x + 1)/((x - 1)**3*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^3*(x-1)^3*F(x)+2*x^8-2*x^7-6*x^6+17*x^5-35*x^4+42*x^3-26*x^2+8*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{3} \left(x -1\right)^{3} F \! \left(x \right)+2 x^{8}-2 x^{7}-6 x^{6}+17 x^{5}-35 x^{4}+42 x^{3}-26 x^{2}+8 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,1/32*(n^2+9*n+4)*2^n-1/2*n^2-1/2*n+2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ \frac{\left(n^{2}+9 n +4\right) 2^{n}}{32}-\frac{n^{2}}{2}-\frac{n}{2}+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) = 61
a(6) = 169
a(7) = 438
a(8) = 1086
a(n+3) = 1/2*n^2+8*a(n)-12*a(n+1)+6*a(n+2)-5/2*n-2, n >= 9
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) = 61
a \! \left(6\right) = 169
a \! \left(7\right) = 438
a \! \left(8\right) = 1086
a \! \left(n +3\right) = \frac{n^{2}}{2}+8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)-\frac{5 n}{2}-2, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15521/
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[38,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[24,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[12,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]+F[26,x]+F[37,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[10,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[10,x]*F[12,x]
F[31,x] = F[24,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]
F[36,x] = F[32,x]
F[37,x] = F[12,x]*F[13,x]
F[38,x] = F[39,x]+F[52,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[1,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[42,x]
F[45,x] = F[39,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[12,x]
F[50,x] = F[51,x]
F[51,x] = F[47,x]
F[52,x] = F[25,x]+F[53,x]+F[72,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[55,x]+F[60,x]
F[55,x] = F[10,x]+F[56,x]
F[56,x] = F[25,x]+F[57,x]+F[58,x]
F[57,x] = F[12,x]*F[55,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[43,x]+F[56,x]
F[60,x] = F[61,x]+F[64,x]
F[61,x] = F[25,x]+F[53,x]+F[62,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[39,x]+F[61,x]
F[64,x] = 2*F[25,x]+F[65,x]+F[70,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[29,x]
F[68,x] = F[69,x]
F[69,x] = F[65,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[46,x]+F[64,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[63,x]+F[74,x]
F[74,x] = F[75,x]+F[91,x]
F[75,x] = F[25,x]+F[76,x]+F[82,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[81,x]
F[78,x] = F[12,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[12,x]*F[43,x]
F[81,x] = F[51,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[39,x]+F[51,x]
F[85,x] = F[75,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[51,x]
F[90,x] = F[86,x]
F[91,x] = F[107,x]+F[25,x]+F[92,x]+F[98,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]+F[97,x]
F[94,x] = F[29,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[12,x]*F[56,x]
F[97,x] = F[69,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[61,x]+F[69,x]
F[101,x] = F[102,x]+F[91,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[69,x]
F[106,x] = F[102,x]
F[107,x] = F[12,x]*F[74,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_{38}\! \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_{24}\! \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_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{37}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{10}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{52}\! \left(x \right)
F_{39}\! \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_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \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_{39}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \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_{12}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \left(x \right)
F_{52}\! \left(x \right) = F_{25}\! \left(x \right)+F_{53}\! \left(x \right)+F_{72}\! \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_{60}\! \left(x \right)
F_{55}\! \left(x \right) = F_{10}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{25}\! \left(x \right)+F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{43}\! \left(x \right)+F_{56}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = F_{25}\! \left(x \right)+F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{39}\! \left(x \right)+F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{65}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{29}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{65}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{46}\! \left(x \right)+F_{64}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{63}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{91}\! \left(x \right)
F_{75}\! \left(x \right) = F_{25}\! \left(x \right)+F_{76}\! \left(x \right)+F_{82}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{81}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{81}\! \left(x \right) = F_{51}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{39}\! \left(x \right)+F_{51}\! \left(x \right)
F_{85}\! \left(x \right) = F_{75}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{51}\! \left(x \right)
F_{90}\! \left(x \right) = F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{107}\! \left(x \right)+F_{25}\! \left(x \right)+F_{92}\! \left(x \right)+F_{98}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{94}\! \left(x \right) = F_{29}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{97}\! \left(x \right) = F_{69}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \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_{61}\! \left(x \right)+F_{69}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{91}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{69}\! \left(x \right)
F_{106}\! \left(x \right) = F_{102}\! \left(x \right)
F_{107}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \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_38(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_24(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_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_12(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_37(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_10(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_10(x)*F_12(x))
Eq(F_31(x), F_24(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x))
Eq(F_36(x), F_32(x))
Eq(F_37(x), F_12(x)*F_13(x))
Eq(F_38(x), F_39(x) + F_52(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_1(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_42(x))
Eq(F_45(x), F_39(x) + F_46(x))
Eq(F_46(x), F_47(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_12(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_47(x))
Eq(F_52(x), F_25(x) + F_53(x) + F_72(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_60(x))
Eq(F_55(x), F_10(x) + F_56(x))
Eq(F_56(x), F_25(x) + F_57(x) + F_58(x))
Eq(F_57(x), F_12(x)*F_55(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_43(x) + F_56(x))
Eq(F_60(x), F_61(x) + F_64(x))
Eq(F_61(x), F_25(x) + F_53(x) + F_62(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_39(x) + F_61(x))
Eq(F_64(x), 2*F_25(x) + F_65(x) + F_70(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_29(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_65(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_46(x) + F_64(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_63(x) + F_74(x))
Eq(F_74(x), F_75(x) + F_91(x))
Eq(F_75(x), F_25(x) + F_76(x) + F_82(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_81(x))
Eq(F_78(x), F_12(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_12(x)*F_43(x))
Eq(F_81(x), F_51(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_39(x) + F_51(x))
Eq(F_85(x), F_75(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_51(x))
Eq(F_90(x), F_86(x))
Eq(F_91(x), F_107(x) + F_25(x) + F_92(x) + F_98(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_97(x))
Eq(F_94(x), F_29(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_12(x)*F_56(x))
Eq(F_97(x), F_69(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_61(x) + F_69(x))
Eq(F_101(x), F_102(x) + F_91(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_69(x))
Eq(F_106(x), F_102(x))
Eq(F_107(x), F_12(x)*F_74(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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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": "comb_spec_searcher.strategies.rule", "comb_class": {"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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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": []}, "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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 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": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 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[[[0, 1], [2, 1]], [[1, 0]]], "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, 2, 3, 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": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 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]]}]]}], "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], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 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": []}, "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, 3, 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": "comb_spec_searcher.strategies.rule", "comb_class": 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{"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 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], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 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]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": 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