0132_1230_2031_2130
Counting sequence:
1, 1, 2, 6, 20, 66, 214, 682, 2144, 6670, 20586, 63150, 192812, 586554, 1779262, 5385106, 16269560, 49084486, 147919314, 445365462, 1339977284, 4029301170, 12110523046, 36386177530, 109290368912, 328189387774, 985336561722, 2957864763006, 8878072843100, 26645030715306, 79961195072014, 239946603254242, 719991948765224, 2160343142338870, 6481916158105506, 19447889232537510, 58348835945143412, 175058985088712994, 525207078020235382, 1575693956822181706, 4727257438743592640, 14182196175546348526, 42547611813547234314, 127645305873773651022, 382941881774493037964, 1148840044062955231770, 3446554893820990015966, 10339748603466694807090, 31019448416039658260312, 93058834381401847218214, 279177684016410860368242, 837535902926926090969206, 2512614591408370611350180, 7537860390357990020800146, 22613621285967318774342214, 67840960703821531933659802, 203523115918197095734187504, 610569912213975862679611870, 1831711099367429238926142426, 5495136588012675594030090270, 16485417706584304187480903612, 49456272294755855250475639434, 148368863176819728532883408302, 445106701290566453849596133506, 1335320373684466060832136707720, 4005961772439038849314052646166, 12017886889901164580860791291714, 36053664466257230475237283104582, 108161002564463212923940301125844, 324483029821326418500932716231170, 973449142885544336459250226212886, 2920347557627699951019766646531050, 8761042984246798817299783952897312, 26283129704438861322022335853192654, 78849390928077212670553459561883562, 236548177165451360290756266684762606, 709644542073554154134947028054817260, 2128933651756282331209293428164622586, 6386801016917286804499463200494738814, 19160403199584359904046007777486129362, 57481209958066518504104842600463084984, 172443630741658932586795784513400561670, 517330894319208990701316686232228995346, 1551992688013550735060289980792752913430, 4655978076246731924034479119262417905412, 13967934258208278972766995633651637973874, 41903802845767083038481712629567841602022, 125711408709053824556470147621793764424506, 377134226541808870671641188060174700190800, 1131402680626473981460410064303201154025406, 3394208044296164080274433938349750975899514, 10182624138723023882055195806052225008798142, 30547872430254877064522579145602766702416924, 91643617324770773671513614882703455540395370, 274930852056410411388789591267346769163497806, 824792556367433557392812144486408268008261410, 2474377669580803409005571921447197127602631912, 7423133009897618023897430111001903990481359094, 22269399032481772402280854514314309510368851682, 66808197104178361664900406252220436216629567206, 200424591328790092241405468356524921559859500340
Generating function in Maple syntax:
(x^5+x^4-2*x^3-6*x^2+5*x-1)/(x-1)/(3*x-1)/(x^2+2*x-1)
Generating function in latex syntax:
\frac{x^{5}+x^{4}-2 x^{3}-6 x^{2}+5 x -1}{\left(x -1\right) \left(3 x -1\right) \left(x^{2}+2 x -1\right)}
Generating function in sympy syntax:
(x**5 + x**4 - 2*x**3 - 6*x**2 + 5*x - 1)/((x - 1)*(3*x - 1)*(x**2 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(x-1)*(3*x-1)*(x^2+2*x-1)*F(x)+x^5+x^4-2*x^3-6*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(3 x -1\right) \left(x^{2}+2 x -1\right) F \! \left(x \right)+x^{5}+x^{4}-2 x^{3}-6 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/2+1/4*(-1-2^(1/2))^(-n)*2^(1/2)-1/4*(2^(1/2)-1)^(-n)*2^(1/2)+7/18*3^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{1}{2}+\frac{\left(-1-\sqrt{2}\right)^{-n} \sqrt{2}}{4}-\frac{\left(\sqrt{2}-1\right)^{-n} \sqrt{2}}{4}+\frac{7 \,3^{n}}{18} & \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) = 66
a(n+3) = -3*a(n)-5*a(n+1)+5*a(n+2)+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) = 66
a \! \left(n +3\right) = -3 a \! \left(n \right)-5 a \! \left(n +1\right)+5 a \! \left(n +2\right)+2, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15627/
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[32,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[21,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[14,x]
F[21,x] = F[22,x]+F[23,x]+F[31,x]
F[22,x] = 0
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[10,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[10,x]*F[12,x]
F[28,x] = F[21,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[12,x]*F[21,x]
F[31,x] = F[12,x]*F[13,x]
F[32,x] = F[33,x]+F[42,x]
F[33,x] = F[34,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[36,x]
F[39,x] = F[33,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[39,x]
F[42,x] = F[108,x]+F[22,x]+F[43,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[45,x]+F[74,x]
F[45,x] = F[46,x]+F[6,x]
F[46,x] = F[22,x]+F[47,x]+F[52,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[10,x]+F[49,x]
F[49,x] = F[22,x]+F[47,x]+F[50,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[37,x]+F[49,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[51,x]+F[54,x]
F[54,x] = F[55,x]+F[64,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[37,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[12,x]*F[37,x]
F[61,x] = F[55,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[12,x]*F[55,x]
F[64,x] = 2*F[22,x]+F[65,x]+F[73,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[67,x]+F[70,x]
F[67,x] = F[49,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[49,x]
F[70,x] = F[64,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[12,x]*F[64,x]
F[73,x] = F[12,x]*F[54,x]
F[74,x] = F[42,x]+F[75,x]
F[75,x] = 2*F[22,x]+F[76,x]+F[86,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[83,x]
F[78,x] = F[22,x]+F[79,x]+F[81,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[48,x]+F[77,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[33,x]+F[78,x]
F[83,x] = 2*F[22,x]+F[76,x]+F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[40,x]+F[83,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[85,x]+F[88,x]
F[88,x] = F[89,x]+F[98,x]
F[89,x] = F[90,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[92,x]+F[95,x]
F[92,x] = F[40,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[12,x]*F[40,x]
F[95,x] = F[89,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[12,x]*F[89,x]
F[98,x] = 3*F[22,x]+F[107,x]+F[99,x]
F[99,x] = F[100,x]*F[12,x]
F[100,x] = F[101,x]+F[104,x]
F[101,x] = F[102,x]+F[83,x]
F[102,x] = F[103,x]
F[103,x] = F[12,x]*F[83,x]
F[104,x] = F[105,x]+F[98,x]
F[105,x] = F[106,x]
F[106,x] = F[12,x]*F[98,x]
F[107,x] = F[12,x]*F[88,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[110,x]+F[82,x]
F[110,x] = F[111,x]+F[120,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[12,x]
F[113,x] = F[114,x]+F[117,x]
F[114,x] = F[115,x]+F[33,x]
F[115,x] = F[116,x]
F[116,x] = F[12,x]*F[33,x]
F[117,x] = F[111,x]+F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[111,x]*F[12,x]
F[120,x] = 2*F[22,x]+F[121,x]+F[129,x]
F[121,x] = F[12,x]*F[122,x]
F[122,x] = F[123,x]+F[126,x]
F[123,x] = F[124,x]+F[78,x]
F[124,x] = F[125,x]
F[125,x] = F[12,x]*F[78,x]
F[126,x] = F[120,x]+F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[12,x]*F[120,x]
F[129,x] = F[110,x]*F[12,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_{32}\! \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_{21}\! \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_{14}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{28}\! \left(x \right) = F_{21}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{42}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{33}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{108}\! \left(x \right)+F_{22}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{74}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{6}\! \left(x \right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right)+F_{47}\! \left(x \right)+F_{52}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{22}\! \left(x \right)+F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{37}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{64}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{37}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{61}\! \left(x \right) = F_{55}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{65}\! \left(x \right)+F_{73}\! \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_{70}\! \left(x \right)
F_{67}\! \left(x \right) = F_{49}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{70}\! \left(x \right) = F_{64}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{74}\! \left(x \right) = F_{42}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{76}\! \left(x \right)+F_{86}\! \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_{83}\! \left(x \right)
F_{78}\! \left(x \right) = F_{22}\! \left(x \right)+F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{48}\! \left(x \right)+F_{77}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{33}\! \left(x \right)+F_{78}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{76}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{40}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{98}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{95}\! \left(x \right)
F_{92}\! \left(x \right) = F_{40}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{95}\! \left(x \right) = F_{89}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{98}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{107}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{104}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{83}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{98}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{107}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{82}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{120}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{12}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{117}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{33}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{117}\! \left(x \right) = F_{111}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{111}\! \left(x \right) F_{12}\! \left(x \right)
F_{120}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{121}\! \left(x \right)+F_{129}\! \left(x \right)
F_{121}\! \left(x \right) = F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{126}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{78}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{126}\! \left(x \right) = F_{120}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right) F_{120}\! \left(x \right)
F_{129}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \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_32(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_21(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_14(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_31(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_10(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_10(x)*F_12(x))
Eq(F_28(x), F_21(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_12(x)*F_21(x))
Eq(F_31(x), F_12(x)*F_13(x))
Eq(F_32(x), F_33(x) + F_42(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_36(x))
Eq(F_39(x), F_33(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_39(x))
Eq(F_42(x), F_108(x) + F_22(x) + F_43(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_74(x))
Eq(F_45(x), F_46(x) + F_6(x))
Eq(F_46(x), F_22(x) + F_47(x) + F_52(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_10(x) + F_49(x))
Eq(F_49(x), F_22(x) + F_47(x) + F_50(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_37(x) + F_49(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_51(x) + F_54(x))
Eq(F_54(x), F_55(x) + F_64(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_37(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_12(x)*F_37(x))
Eq(F_61(x), F_55(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_12(x)*F_55(x))
Eq(F_64(x), 2*F_22(x) + F_65(x) + F_73(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_70(x))
Eq(F_67(x), F_49(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_49(x))
Eq(F_70(x), F_64(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_12(x)*F_64(x))
Eq(F_73(x), F_12(x)*F_54(x))
Eq(F_74(x), F_42(x) + F_75(x))
Eq(F_75(x), 2*F_22(x) + F_76(x) + F_86(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_83(x))
Eq(F_78(x), F_22(x) + F_79(x) + F_81(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_48(x) + F_77(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_33(x) + F_78(x))
Eq(F_83(x), 2*F_22(x) + F_76(x) + F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_40(x) + F_83(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_85(x) + F_88(x))
Eq(F_88(x), F_89(x) + F_98(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_95(x))
Eq(F_92(x), F_40(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_12(x)*F_40(x))
Eq(F_95(x), F_89(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_12(x)*F_89(x))
Eq(F_98(x), F_107(x) + 3*F_22(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_12(x))
Eq(F_100(x), F_101(x) + F_104(x))
Eq(F_101(x), F_102(x) + F_83(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_12(x)*F_83(x))
Eq(F_104(x), F_105(x) + F_98(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_12(x)*F_98(x))
Eq(F_107(x), F_12(x)*F_88(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_82(x))
Eq(F_110(x), F_111(x) + F_120(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_12(x))
Eq(F_113(x), F_114(x) + F_117(x))
Eq(F_114(x), F_115(x) + F_33(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_12(x)*F_33(x))
Eq(F_117(x), F_111(x) + F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_111(x)*F_12(x))
Eq(F_120(x), F_121(x) + F_129(x) + 2*F_22(x))
Eq(F_121(x), F_12(x)*F_122(x))
Eq(F_122(x), F_123(x) + F_126(x))
Eq(F_123(x), F_124(x) + F_78(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_12(x)*F_78(x))
Eq(F_126(x), F_120(x) + F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_12(x)*F_120(x))
Eq(F_129(x), F_110(x)*F_12(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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 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, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[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": [2, 1, 3, 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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 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": [2, 1, 3, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": 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