0231_1032_1203_1302_2130
Counting sequence:
1, 1, 2, 6, 19, 57, 167, 483, 1384, 3936, 11123, 31263, 87457, 243651, 676334, 1871322, 5162707, 14206053, 38998139, 106827171, 292057108, 797026548, 2171495987, 5907199371, 16046842549, 43533811587, 117959301722, 319257738798, 863150140819, 2331287716881, 6290661883343, 16959449520483, 45683992566592, 122962694257416, 330718282551539, 888864564356727, 2387378451051337, 6408107499435843, 17189951138639174, 46085930479992066, 123487386900485203, 330710685455397693, 885228488568362147, 2368391782323717411, 6333614045522221804, 16930034913527214492, 45235577185792789427, 120816371556766990563, 322553475732522324829, 860824195471926574851, 2296519591928623029938, 6124555884218912814678, 16328011491197660683027, 43516247576877734741481, 115940174771476994793719, 308805838346173937889507, 822262581560865432371992, 2188836068609263511468208, 5825022869791627945260659, 15497710115066887701756111, 41221762952788134449106673, 109617067601133546135418563, 291424250946741496137613982, 774590629669641888328963626, 2058357660257708014823432659, 5468577473259502748012261397, 14525650103793338158851976907, 38575103748782104925588618403, 102421578530265218279410100164, 271888653094488681700085398596, 721619527122913980521681023283, 1914896346130917589180018737723, 5080473618470118621262723461637, 13476810413023613448026135395971, 35743411224632967408825285700874, 94783498169227850663060546881662, 251303854404076024548179227494547, 666188303497723981000334928078273, 1765745000332241752541576061618719, 4679438291773715020871786978936931, 12399260713569898708727215536790768, 32850024770404253557022757894072408, 87019165523466683918826322271738867, 230480846655998991617199103037444391, 610375147086716049229514405063182489, 1616226537674703237543831472703567427, 4279098522506870149522698676479324662, 11327869256483782587913933186478356818, 29984115870288627258767388108755791699, 79356497997776672745143424187445205741, 210001830429880962002380176370748342003, 555666330568990352782393787628649182243, 1470132720801622943880273942709578774172, 3889121173132352881944449626379376486636, 10287263262960326063675666937872039155379, 27208376667546821991164305605687917042067, 71954958430709839594339921133101751688877, 190272065645873599163341717136896281116163, 503090847879753965325621337053513881216354, 1330073739090626416731844355008146788111526, 3516120543310996637194941804148503970297363
Generating function in Maple syntax:
-(x-1)*(2*x^4+2*x^3+3*x^2-4*x+1)/(x^2-3*x+1)^2
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(2 x^{4}+2 x^{3}+3 x^{2}-4 x +1\right)}{\left(x^{2}-3 x +1\right)^{2}}
Generating function in sympy syntax:
(1 - x)*(2*x**4 + 2*x**3 + 3*x**2 - 4*x + 1)/(x**2 - 3*x + 1)**2
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)^2*F(x)+(x-1)*(2*x^4+2*x^3+3*x^2-4*x+1) = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)+\left(x -1\right) \left(2 x^{4}+2 x^{3}+3 x^{2}-4 x +1\right) = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/50*((-75*n+141)*5^(1/2)-165*n+325)*(3/2+1/2*5^(1/2))^(-n)+3/2*((n-47/25)*5^(1/2)-11/5*n+13/3)*(3/2-1/2*5^(1/2))^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(\left(-75 n +141\right) \sqrt{5}-165 n +325\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{50}+\\\frac{3 \left(\left(n -\frac{47}{25}\right) \sqrt{5}-\frac{11 n}{5}+\frac{13}{3}\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{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) = 19
a(5) = 57
a(n+4) = -a(n)+6*a(n+1)-11*a(n+2)+6*a(n+3), 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) = 19
a \! \left(5\right) = 57
a \! \left(n +4\right) = -a \! \left(n \right)+6 a \! \left(n +1\right)-11 a \! \left(n +2\right)+6 a \! \left(n +3\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://www.permpal.com/tree/22017/
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[9,x]
F[4,x] = F[14,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[10,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[5,x]
F[11,x] = F[12,x]*F[7,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[12,x]*F[9,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[5,x]*F[9,x]
F[16,x] = F[17,x]+F[56,x]
F[17,x] = F[18,x]+F[32,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[9,x]
F[21,x] = F[22,x]+F[27,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[9,x]
F[25,x] = F[22,x]+F[26,x]
F[26,x] = F[23,x]
F[27,x] = F[19,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[9,x]
F[30,x] = F[27,x]+F[31,x]
F[31,x] = F[28,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[13,x]
F[34,x] = F[35,x]+F[36,x]+F[44,x]
F[35,x] = 0
F[36,x] = F[37,x]*F[9,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[39,x]
F[39,x] = F[40,x]*F[9,x]
F[40,x] = F[1,x]+F[38,x]
F[41,x] = F[35,x]+F[36,x]+F[42,x]
F[42,x] = F[43,x]*F[9,x]
F[43,x] = F[33,x]+F[41,x]
F[44,x] = F[45,x]*F[9,x]
F[45,x] = F[46,x]+F[51,x]
F[46,x] = F[33,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]*F[9,x]
F[49,x] = F[46,x]+F[50,x]
F[50,x] = F[47,x]
F[51,x] = F[34,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]*F[9,x]
F[54,x] = F[51,x]+F[55,x]
F[55,x] = F[52,x]
F[56,x] = F[57,x]+F[80,x]
F[57,x] = F[33,x]+F[58,x]
F[58,x] = F[35,x]+F[36,x]+F[59,x]
F[59,x] = F[60,x]*F[9,x]
F[60,x] = F[61,x]+F[67,x]
F[61,x] = F[33,x]+F[62,x]
F[62,x] = F[35,x]+F[48,x]+F[63,x]
F[63,x] = F[64,x]*F[9,x]
F[64,x] = F[65,x]+F[9,x]
F[65,x] = F[35,x]+F[63,x]+F[66,x]
F[66,x] = F[33,x]*F[9,x]
F[67,x] = F[58,x]+F[68,x]
F[68,x] = 2*F[35,x]+F[69,x]+F[75,x]
F[69,x] = F[70,x]*F[9,x]
F[70,x] = F[71,x]+F[73,x]
F[71,x] = F[72,x]
F[72,x] = F[38,x]*F[9,x]
F[73,x] = 2*F[35,x]+F[69,x]+F[74,x]
F[74,x] = F[41,x]*F[9,x]
F[75,x] = F[76,x]*F[9,x]
F[76,x] = F[77,x]+F[79,x]
F[77,x] = F[58,x]+F[78,x]
F[78,x] = F[75,x]
F[79,x] = F[78,x]
F[80,x] = F[81,x]+F[84,x]
F[81,x] = F[82,x]
F[82,x] = F[83,x]*F[9,x]
F[83,x] = F[33,x]
F[84,x] = F[85,x]
F[85,x] = F[86,x]*F[9,x]
F[86,x] = F[87,x]+F[94,x]
F[87,x] = F[81,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[9,x]*F[90,x]
F[90,x] = F[91,x]+F[93,x]
F[91,x] = F[81,x]+F[92,x]
F[92,x] = F[89,x]
F[93,x] = F[92,x]
F[94,x] = F[84,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[9,x]*F[97,x]
F[97,x] = F[100,x]+F[98,x]
F[98,x] = F[84,x]+F[99,x]
F[99,x] = F[96,x]
F[100,x] = F[99,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_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \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_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{5}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{56}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{32}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{9}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{28}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{13}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{44}\! \left(x \right)
F_{35}\! \left(x \right) = 0
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{9}\! \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_{40}\! \left(x \right) F_{9}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right) F_{9}\! \left(x \right)
F_{43}\! \left(x \right) = F_{33}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right) F_{9}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{51}\! \left(x \right)
F_{46}\! \left(x \right) = F_{33}\! \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_{9}\! \left(x \right)
F_{49}\! \left(x \right) = F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{34}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{9}\! \left(x \right)
F_{54}\! \left(x \right) = F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{52}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{80}\! \left(x \right)
F_{57}\! \left(x \right) = F_{33}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right) F_{9}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{67}\! \left(x \right)
F_{61}\! \left(x \right) = F_{33}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{35}\! \left(x \right)+F_{48}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right) F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{9}\! \left(x \right)
F_{65}\! \left(x \right) = F_{35}\! \left(x \right)+F_{63}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{33}\! \left(x \right) F_{9}\! \left(x \right)
F_{67}\! \left(x \right) = F_{58}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right) F_{9}\! \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) = F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{41}\! \left(x \right) F_{9}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right) F_{9}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{58}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{75}\! \left(x \right)
F_{79}\! \left(x \right) = F_{78}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right) F_{9}\! \left(x \right)
F_{83}\! \left(x \right) = F_{33}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right) F_{9}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{94}\! \left(x \right)
F_{87}\! \left(x \right) = F_{81}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{9}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{93}\! \left(x \right)
F_{91}\! \left(x \right) = F_{81}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{89}\! \left(x \right)
F_{93}\! \left(x \right) = F_{92}\! \left(x \right)
F_{94}\! \left(x \right) = F_{84}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{9}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{84}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{96}\! \left(x \right)
F_{100}\! \left(x \right) = F_{99}\! \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_9(x))
Eq(F_4(x), F_14(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_8(x))
Eq(F_8(x), F_10(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_5(x))
Eq(F_11(x), F_12(x)*F_7(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_12(x)*F_9(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_5(x)*F_9(x))
Eq(F_16(x), F_17(x) + F_56(x))
Eq(F_17(x), F_18(x) + F_32(x))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_9(x))
Eq(F_21(x), F_22(x) + F_27(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_9(x))
Eq(F_25(x), F_22(x) + F_26(x))
Eq(F_26(x), F_23(x))
Eq(F_27(x), F_19(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_9(x))
Eq(F_30(x), F_27(x) + F_31(x))
Eq(F_31(x), F_28(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_13(x))
Eq(F_34(x), F_35(x) + F_36(x) + F_44(x))
Eq(F_35(x), 0)
Eq(F_36(x), F_37(x)*F_9(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_40(x)*F_9(x))
Eq(F_40(x), F_1(x) + F_38(x))
Eq(F_41(x), F_35(x) + F_36(x) + F_42(x))
Eq(F_42(x), F_43(x)*F_9(x))
Eq(F_43(x), F_33(x) + F_41(x))
Eq(F_44(x), F_45(x)*F_9(x))
Eq(F_45(x), F_46(x) + F_51(x))
Eq(F_46(x), F_33(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x)*F_9(x))
Eq(F_49(x), F_46(x) + F_50(x))
Eq(F_50(x), F_47(x))
Eq(F_51(x), F_34(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x)*F_9(x))
Eq(F_54(x), F_51(x) + F_55(x))
Eq(F_55(x), F_52(x))
Eq(F_56(x), F_57(x) + F_80(x))
Eq(F_57(x), F_33(x) + F_58(x))
Eq(F_58(x), F_35(x) + F_36(x) + F_59(x))
Eq(F_59(x), F_60(x)*F_9(x))
Eq(F_60(x), F_61(x) + F_67(x))
Eq(F_61(x), F_33(x) + F_62(x))
Eq(F_62(x), F_35(x) + F_48(x) + F_63(x))
Eq(F_63(x), F_64(x)*F_9(x))
Eq(F_64(x), F_65(x) + F_9(x))
Eq(F_65(x), F_35(x) + F_63(x) + F_66(x))
Eq(F_66(x), F_33(x)*F_9(x))
Eq(F_67(x), F_58(x) + F_68(x))
Eq(F_68(x), 2*F_35(x) + F_69(x) + F_75(x))
Eq(F_69(x), F_70(x)*F_9(x))
Eq(F_70(x), F_71(x) + F_73(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_38(x)*F_9(x))
Eq(F_73(x), 2*F_35(x) + F_69(x) + F_74(x))
Eq(F_74(x), F_41(x)*F_9(x))
Eq(F_75(x), F_76(x)*F_9(x))
Eq(F_76(x), F_77(x) + F_79(x))
Eq(F_77(x), F_58(x) + F_78(x))
Eq(F_78(x), F_75(x))
Eq(F_79(x), F_78(x))
Eq(F_80(x), F_81(x) + F_84(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x)*F_9(x))
Eq(F_83(x), F_33(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_86(x)*F_9(x))
Eq(F_86(x), F_87(x) + F_94(x))
Eq(F_87(x), F_81(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_9(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_93(x))
Eq(F_91(x), F_81(x) + F_92(x))
Eq(F_92(x), F_89(x))
Eq(F_93(x), F_92(x))
Eq(F_94(x), F_84(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_9(x)*F_97(x))
Eq(F_97(x), F_100(x) + F_98(x))
Eq(F_98(x), F_84(x) + F_99(x))
Eq(F_99(x), F_96(x))
Eq(F_100(x), F_99(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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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"pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [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, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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"pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 4], [0, 4], [0, 0], [0, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 4], [0, 4], [0, 0], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2], [0, 4]], [[1, 3]], [[2, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": 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