01342_01423_01432_02341_02413_02431_03241_03412_03421_04231_04312_04321_10342_10423_10432_12340_12403_12430_13240_13402_13420_14230_14302_14320_20341_20413_20431_21340_21403_21430_23401_23410_24301_24310_30412_30421_31402_31420_32401_32410

Counting sequence:
1, 1, 2, 6, 24, 80, 264, 856, 2776, 8984, 29080, 94104, 304536, 985496, 3189144, 10320280, 33397144, 108075416, 349739416, 1131780504, 3662518680, 11852159384, 38354393496, 124117424536, 401652423064, 1299774544280, 4206158780824, 13611415738776, 44047466600856, 142540596156824, 461271058717080, 1492704502061464, 4830493238991256, 15631804486228376, 50585581928421784, 163698381801757080, 529739091317201304, 1714271709841430936, 5547499784951667096, 17952086409269057944, 58094171958344784280, 187996689553765800344, 608370066940910737816, 1968726892096884677016, 6370934051957412305304, 20616775672302363318680, 66717287552434375858584, 215901677794078204991896, 698672505797893913418136, 2260951722772100646803864, 7316593468735776947280280, 23676993828559956481776024, 76620361532063020752673176, 247948698378365867432450456, 802378842884983817875593624, 2596552479283431105480989080, 8402620330106797482464352664, 27191450577347319386852661656, 87993382475121828703562733976, 284752567259632934954536114584, 921478664419753184723323165080, 2981967597878038109264790788504, 9649849853435088957422874237336, 31227570098382330351904911628696, 101054539610505016533501320206744, 327019359614539354474622286928280, 1058256877671098775083249854683544, 3424591193800354968064988857080216, 11082209898285105036462977132894616, 35862784571771629945185909694110104, 116054408736683680036223727919798680, 375559955760453879853191094616037784, 1215337546467642479851277100911270296, 3932914915977100479115318580286691736, 12727180017824770877635745564218464664, 41186019699557943671732765449583696280, 133280759470414970854008513156041251224, 431305597739061716394948088110417287576, 1395734233359783316205930228844999580056, 4516690857675813497991652810131668310424, 14616318648790760260807026535643334941080, 47299400728284774513580664311813343123864, 153064076051732590070389434766200026012056, 495325755016604278195101526779653424519576, 1602907814240138916671760792624106953087384, 5187118648546694946123927692366827604253080, 16785868554053945558934898555230083020855704, 54320211702294670902365507879927476458723736, 175783897620805124040470609980775285000870296, 568848642050788931690403251481260475836635544, 1840832874584798359542688942885622091676752280, 5957060317372752445846990891696286086700046744, 19277452133084698329864737554935060540107102616, 62383145535660406443117438676655265427014392216, 201876099603659606205693827573050773014457194904, 653284781349960838183857409852722607736971958680, 2114073961114560101190490129997648307531772696984, 6841287047628963555116409899406187046011433228696, 22138869939716167514994780318802967322149957245336, 71642888069948189250455200235230682828345647405464, 231841255898761048560889521745673234945291123792280

Generating function in Maple syntax:
(2*x-1)*(x+1)*(2*x^3+2*x^2+x-1)/(x-1)/(4*x^2+2*x-1)

Generating function in latex syntax:
\frac{\left(2 x -1\right) \left(x +1\right) \left(2 x^{3}+2 x^{2}+x -1\right)}{\left(x -1\right) \left(4 x^{2}+2 x -1\right)}

Generating function in sympy syntax:
(x + 1)*(2*x - 1)*(2*x**3 + 2*x**2 + x - 1)/((x - 1)*(4*x**2 + 2*x - 1))

Implicit equation for the generating function in Maple syntax:
-(x-1)*(4*x^2+2*x-1)*F(x)+(2*x-1)*(x+1)*(2*x^3+2*x^2+x-1) = 0

Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(4 x^{2}+2 x -1\right) F \! \left(x \right)+\left(2 x -1\right) \left(x +1\right) \left(2 x^{3}+2 x^{2}+x -1\right) = 0

Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,1/40*(-5^(1/2)+7)*(-1/4*5^(1/2)-1/4)^(-n)-8/5+1/40*(5^(1/2)+7)*(1/4*5^(1/2)-1/4)^(-n))

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ \frac{\left(-\sqrt{5}+7\right) \left(-\frac{\sqrt{5}}{4}-\frac{1}{4}\right)^{-n}}{40}-\frac{8}{5}+\frac{\left(\sqrt{5}+7\right) \left(\frac{\sqrt{5}}{4}-\frac{1}{4}\right)^{-n}}{40} & \mathit{\text{otherwise}} \end{array}\right.

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a(n+2) = 4*a(n)+2*a(n+1)+8, n >= 6

Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a{\left(n + 2 \right)} = 4 a{\left(n \right)} + 2 a{\left(n + 1 \right)} + 8, \quad n \geq 6

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/25609/
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[14,x]*F[4,x]
F[4,x] = F[40,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[17,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[14,x]
F[12,x] = F[13,x]+F[9,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = x
F[15,x] = F[16,x]
F[16,x] = F[10,x]*F[14,x]
F[17,x] = F[18,x]+F[23,x]
F[18,x] = F[19,x]
F[19,x] = F[14,x]*F[20,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[1,x]+F[14,x]
F[22,x] = F[14,x]
F[23,x] = F[24,x]+F[25,x]+F[30,x]
F[24,x] = 0
F[25,x] = F[14,x]*F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[10,x]+F[15,x]
F[28,x] = F[29,x]
F[29,x] = F[16,x]+F[24,x]+F[30,x]
F[30,x] = F[14,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[14,x]+F[29,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[24,x]+F[35,x]+F[36,x]
F[35,x] = x^2
F[36,x] = x^2
F[37,x] = 2*F[24,x]+F[38,x]+F[39,x]
F[38,x] = F[14,x]*F[15,x]
F[39,x] = F[14,x]*F[29,x]
F[40,x] = F[41,x]+F[65,x]
F[41,x] = F[42,x]
F[42,x] = F[14,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[1,x]+F[18,x]
F[45,x] = F[46,x]+F[52,x]
F[46,x] = F[47,x]
F[47,x] = F[14,x]*F[48,x]
F[48,x] = F[21,x]+F[49,x]
F[49,x] = F[46,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[14,x]*F[46,x]
F[52,x] = F[24,x]+F[53,x]+F[61,x]
F[53,x] = F[14,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[14,x]+F[34,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[24,x]+F[51,x]+F[53,x]
F[58,x] = 2*F[24,x]+F[59,x]+F[60,x]
F[59,x] = F[14,x]*F[57,x]
F[60,x] = F[14,x]*F[50,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[46,x]+F[57,x]
F[64,x] = F[50,x]
F[65,x] = F[24,x]+F[66,x]+F[98,x]
F[66,x] = F[14,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[10,x]+F[23,x]
F[69,x] = F[70,x]+F[93,x]
F[70,x] = F[24,x]+F[71,x]+F[89,x]
F[71,x] = F[14,x]*F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[10,x]+F[29,x]
F[74,x] = F[70,x]+F[75,x]
F[75,x] = 2*F[24,x]+F[76,x]+F[77,x]
F[76,x] = F[14,x]*F[70,x]
F[77,x] = F[14,x]*F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[50,x]+F[75,x]
F[80,x] = F[58,x]+F[81,x]
F[81,x] = 3*F[24,x]+F[82,x]+F[88,x]
F[82,x] = F[14,x]*F[83,x]
F[83,x] = 2*F[24,x]+F[76,x]+F[84,x]
F[84,x] = F[14,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[15,x]+F[37,x]
F[87,x] = F[81,x]+F[83,x]
F[88,x] = F[14,x]*F[75,x]
F[89,x] = F[14,x]*F[90,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[46,x]+F[70,x]
F[92,x] = F[57,x]+F[83,x]
F[93,x] = F[24,x]+F[77,x]+F[84,x]+F[94,x]
F[94,x] = F[14,x]*F[95,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[70,x]+F[83,x]
F[97,x] = F[75,x]
F[98,x] = F[14,x]*F[99,x]
F[99,x] = F[100,x]+F[91,x]
F[100,x] = F[52,x]+F[93,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{40}\! \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_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{17}\! \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_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{22}\! \left(x \right) = F_{14}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{30}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right)+F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{14}\! \left(x \right)+F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{24}\! \left(x \right)+F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = x^{2}
F_{36}\! \left(x \right) = x^{2}
F_{37}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right) F_{29}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{65}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{52}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{21}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{52}\! \left(x \right) = F_{24}\! \left(x \right)+F_{53}\! \left(x \right)+F_{61}\! \left(x \right)
F_{53}\! \left(x \right) = F_{14}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right)+F_{34}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{24}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right) F_{50}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{46}\! \left(x \right)+F_{57}\! \left(x \right)
F_{64}\! \left(x \right) = F_{50}\! \left(x \right)
F_{65}\! \left(x \right) = F_{24}\! \left(x \right)+F_{66}\! \left(x \right)+F_{98}\! \left(x \right)
F_{66}\! \left(x \right) = F_{14}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{93}\! \left(x \right)
F_{70}\! \left(x \right) = F_{24}\! \left(x \right)+F_{71}\! \left(x \right)+F_{89}\! \left(x \right)
F_{71}\! \left(x \right) = F_{14}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{10}\! \left(x \right)+F_{29}\! \left(x \right)
F_{74}\! \left(x \right) = F_{70}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{70}\! \left(x \right)
F_{77}\! \left(x \right) = F_{14}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{50}\! \left(x \right)+F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{58}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 3 F_{24}\! \left(x \right)+F_{82}\! \left(x \right)+F_{88}\! \left(x \right)
F_{82}\! \left(x \right) = F_{14}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{76}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right)+F_{37}\! \left(x \right)
F_{87}\! \left(x \right) = F_{81}\! \left(x \right)+F_{83}\! \left(x \right)
F_{88}\! \left(x \right) = F_{14}\! \left(x \right) F_{75}\! \left(x \right)
F_{89}\! \left(x \right) = F_{14}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{46}\! \left(x \right)+F_{70}\! \left(x \right)
F_{92}\! \left(x \right) = F_{57}\! \left(x \right)+F_{83}\! \left(x \right)
F_{93}\! \left(x \right) = F_{24}\! \left(x \right)+F_{77}\! \left(x \right)+F_{84}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{14}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{70}\! \left(x \right)+F_{83}\! \left(x \right)
F_{97}\! \left(x \right) = F_{75}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{91}\! \left(x \right)
F_{100}\! \left(x \right) = F_{52}\! \left(x \right)+F_{93}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_40(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_14(x)*F_8(x))
Eq(F_8(x), F_17(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_14(x))
Eq(F_12(x), F_13(x) + F_9(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_10(x)*F_14(x))
Eq(F_17(x), F_18(x) + F_23(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_14(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_1(x) + F_14(x))
Eq(F_22(x), F_14(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_30(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_14(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_10(x) + F_15(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_16(x) + F_24(x) + F_30(x))
Eq(F_30(x), F_14(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_14(x) + F_29(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_24(x) + F_35(x) + F_36(x))
Eq(F_35(x), x**2)
Eq(F_36(x), x**2)
Eq(F_37(x), 2*F_24(x) + F_38(x) + F_39(x))
Eq(F_38(x), F_14(x)*F_15(x))
Eq(F_39(x), F_14(x)*F_29(x))
Eq(F_40(x), F_41(x) + F_65(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_14(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_1(x) + F_18(x))
Eq(F_45(x), F_46(x) + F_52(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_14(x)*F_48(x))
Eq(F_48(x), F_21(x) + F_49(x))
Eq(F_49(x), F_46(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_14(x)*F_46(x))
Eq(F_52(x), F_24(x) + F_53(x) + F_61(x))
Eq(F_53(x), F_14(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_14(x) + F_34(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_24(x) + F_51(x) + F_53(x))
Eq(F_58(x), 2*F_24(x) + F_59(x) + F_60(x))
Eq(F_59(x), F_14(x)*F_57(x))
Eq(F_60(x), F_14(x)*F_50(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_46(x) + F_57(x))
Eq(F_64(x), F_50(x))
Eq(F_65(x), F_24(x) + F_66(x) + F_98(x))
Eq(F_66(x), F_14(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_10(x) + F_23(x))
Eq(F_69(x), F_70(x) + F_93(x))
Eq(F_70(x), F_24(x) + F_71(x) + F_89(x))
Eq(F_71(x), F_14(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_10(x) + F_29(x))
Eq(F_74(x), F_70(x) + F_75(x))
Eq(F_75(x), 2*F_24(x) + F_76(x) + F_77(x))
Eq(F_76(x), F_14(x)*F_70(x))
Eq(F_77(x), F_14(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_50(x) + F_75(x))
Eq(F_80(x), F_58(x) + F_81(x))
Eq(F_81(x), 3*F_24(x) + F_82(x) + F_88(x))
Eq(F_82(x), F_14(x)*F_83(x))
Eq(F_83(x), 2*F_24(x) + F_76(x) + F_84(x))
Eq(F_84(x), F_14(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_15(x) + F_37(x))
Eq(F_87(x), F_81(x) + F_83(x))
Eq(F_88(x), F_14(x)*F_75(x))
Eq(F_89(x), F_14(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_46(x) + F_70(x))
Eq(F_92(x), F_57(x) + F_83(x))
Eq(F_93(x), F_24(x) + F_77(x) + F_84(x) + F_94(x))
Eq(F_94(x), F_14(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_70(x) + F_83(x))
Eq(F_97(x), F_75(x))
Eq(F_98(x), F_14(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_91(x))
Eq(F_100(x), F_52(x) + F_93(x))
Pack JSON:
{"name": "point_placements", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 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