0213_1230_1302_2301
Counting sequence:
1, 1, 2, 6, 20, 63, 185, 513, 1359, 3468, 8578, 20668, 48710, 112685, 256639, 576843, 1282209, 2823314, 6166832, 13377166, 28845248, 61877211, 132133877, 281034021, 595609475, 1258312488, 2650824750, 5570064048, 11676974794, 24427663513, 51002778683, 106300488143, 221190869365, 459561560910, 953482807164, 1975685031458, 4088808949604, 8452495731559, 17454747193937, 36009005923401, 74217035000183, 152832116398596, 314460325695002, 646512837297636, 1328210046534030, 2726788837081413, 5594315162338615, 11470105301192083, 23503160555592329, 48132221017795658, 98516241849025288, 201536083325148918, 412079365904744520, 842173130318653235, 1720375057655927789, 3512807709349414573, 7169730606774288299, 14627691589699862304, 29831843931702691142, 60816609368011739736, 123939061745236649618, 252489809508900127281, 514202991054654432627, 1046852726183017779351, 2130598940513453982685, 4334984857321745448838, 8817543667233166541780, 17930235239645685092618, 36450766289650074969964, 74082124200017560323903, 150525431641469942280393, 305773229765809528742993, 620991192497358346822175, 1260871850926195273345660, 2559522633715347707182514, 5194603131156609736498188, 10540321989765048118478294, 21382875434433753529203549, 43370213778674821644254447, 87949353376964272461630171, 178316558393157803271005553, 361468820064774123239083266, 732609046686465279873974752, 1484560906486764626541315166, 3007807439201197386671199440, 6092986130857731040521466763, 12340714766626134615403094245, 24990914543073614299528633653, 50600799105789918736504383699, 102439538250865217747905332248, 207354956580301196045606235998, 419661673317743913190806170368, 849226866949770868580802410330, 1718260774528107821559987754185, 3476135630313347811916744295339, 7031499423140959961427029214303, 14221455171310448598041142859589, 28759822992677954546456457903294, 58153471285470023793661263639852, 117574593171168276988819226558706, 237684487542793012780631855439988
Generating function in Maple syntax:
(2*x^7-11*x^6+29*x^5-49*x^4+48*x^3-27*x^2+8*x-1)/(2*x-1)^2/(x-1)^5
Generating function in latex syntax:
\frac{2 x^{7}-11 x^{6}+29 x^{5}-49 x^{4}+48 x^{3}-27 x^{2}+8 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{5}}
Generating function in sympy syntax:
(2*x**7 - 11*x**6 + 29*x**5 - 49*x**4 + 48*x**3 - 27*x**2 + 8*x - 1)/((x - 1)**5*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x-1)^5*F(x)-2*x^7+11*x^6-29*x^5+49*x^4-48*x^3+27*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x -1\right)^{5} F \! \left(x \right)-2 x^{7}+11 x^{6}-29 x^{5}+49 x^{4}-48 x^{3}+27 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,13+2^(n+1)*n-25*2^(-1+n)+35/24*n^2+29/4*n+1/4*n^3+1/24*n^4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 13+2^{n +1} n -25 \,2^{-1+n}+\frac{35 n^{2}}{24}+\frac{29 n}{4}+\frac{n^{3}}{4}+\frac{n^{4}}{24} & \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) = 63
a(6) = 185
a(7) = 513
a(n+2) = -4*a(n)+4*a(n+1)+1/24*n*(n^3-2*n^2-n+50), n >= 8
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 63
a \! \left(6\right) = 185
a \! \left(7\right) = 513
a \! \left(n +2\right) = -4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{n \left(n^{3}-2 n^{2}-n +50\right)}{24}, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21388/
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[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[14,x]*F[7,x]
F[7,x] = F[28,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[20,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[14,x]
F[14,x] = x
F[15,x] = F[12,x]+F[16,x]
F[16,x] = F[17,x]^2
F[17,x] = F[18,x]
F[18,x] = F[14,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[14,x]*F[23,x]
F[23,x] = F[20,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[14,x]*F[26,x]
F[26,x] = F[23,x]+F[27,x]
F[27,x] = F[17,x]*F[19,x]
F[28,x] = F[19,x]*F[29,x]
F[29,x] = F[30,x]+F[83,x]
F[30,x] = F[17,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]+F[58,x]
F[32,x] = 0
F[33,x] = F[14,x]*F[34,x]
F[34,x] = F[35,x]+F[42,x]
F[35,x] = F[17,x]+F[36,x]
F[36,x] = F[32,x]+F[37,x]+F[38,x]
F[37,x] = F[14,x]*F[35,x]
F[38,x] = F[14,x]*F[39,x]
F[39,x] = F[14,x]+F[40,x]
F[40,x] = F[32,x]+F[38,x]+F[41,x]
F[41,x] = F[14,x]*F[17,x]
F[42,x] = F[43,x]+F[60,x]
F[43,x] = F[32,x]+F[44,x]+F[58,x]
F[44,x] = F[14,x]*F[45,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[17,x]+F[47,x]
F[47,x] = F[41,x]
F[48,x] = F[43,x]+F[49,x]
F[49,x] = 2*F[32,x]+F[50,x]+F[54,x]
F[50,x] = F[14,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[47,x]
F[53,x] = F[49,x]
F[54,x] = F[14,x]*F[55,x]
F[55,x] = F[32,x]+F[56,x]+F[58,x]
F[56,x] = F[14,x]*F[57,x]
F[57,x] = F[17,x]+F[55,x]
F[58,x] = F[14,x]*F[59,x]
F[59,x] = F[17,x]+F[55,x]
F[60,x] = F[32,x]+F[61,x]+F[76,x]+F[78,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = F[63,x]+F[66,x]
F[63,x] = F[36,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[14,x]*F[36,x]
F[66,x] = F[60,x]+F[67,x]
F[67,x] = 3*F[32,x]+F[68,x]+F[72,x]
F[68,x] = F[14,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[64,x]
F[71,x] = F[67,x]
F[72,x] = F[14,x]*F[73,x]
F[73,x] = F[32,x]+F[74,x]+F[76,x]+F[78,x]
F[74,x] = F[14,x]*F[75,x]
F[75,x] = F[36,x]+F[73,x]
F[76,x] = F[14,x]*F[77,x]
F[77,x] = F[55,x]+F[73,x]
F[78,x] = F[14,x]*F[79,x]
F[79,x] = F[80,x]+F[82,x]
F[80,x] = F[81,x]
F[81,x] = F[14,x]*F[17,x]
F[82,x] = 2*F[32,x]+F[54,x]+F[78,x]
F[83,x] = F[84,x]
F[84,x] = F[14,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[17,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[14,x]*F[86,x]
F[89,x] = F[102,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[14,x]*F[92,x]
F[92,x] = F[46,x]+F[93,x]
F[93,x] = F[90,x]+F[94,x]
F[94,x] = 2*F[32,x]+F[95,x]+F[98,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[52,x]+F[97,x]
F[97,x] = F[94,x]
F[98,x] = F[14,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[14,x]
F[101,x] = F[17,x]+F[99,x]
F[102,x] = 2*F[32,x]+F[103,x]+F[118,x]
F[103,x] = F[104,x]*F[14,x]
F[104,x] = F[105,x]+F[108,x]
F[105,x] = F[106,x]+F[87,x]
F[106,x] = F[107,x]
F[107,x] = F[14,x]*F[87,x]
F[108,x] = F[102,x]+F[109,x]
F[109,x] = 3*F[32,x]+F[110,x]+F[114,x]
F[110,x] = F[111,x]*F[14,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[106,x]
F[113,x] = F[109,x]
F[114,x] = F[115,x]*F[14,x]
F[115,x] = 2*F[32,x]+F[116,x]+F[118,x]
F[116,x] = F[117,x]*F[14,x]
F[117,x] = F[115,x]+F[87,x]
F[118,x] = F[119,x]*F[14,x]
F[119,x] = F[115,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{28}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
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)^{2}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{14}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{83}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{58}\! \left(x \right)
F_{32}\! \left(x \right) = 0
F_{33}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{42}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)+F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{32}\! \left(x \right)+F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{60}\! \left(x \right)
F_{43}\! \left(x \right) = F_{32}\! \left(x \right)+F_{44}\! \left(x \right)+F_{58}\! \left(x \right)
F_{44}\! \left(x \right) = F_{14}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{17}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{41}\! \left(x \right)
F_{48}\! \left(x \right) = F_{43}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{50}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{47}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49}\! \left(x \right)
F_{54}\! \left(x \right) = F_{14}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{32}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{14}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{17}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{14}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{17}\! \left(x \right)+F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{32}\! \left(x \right)+F_{61}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \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_{66}\! \left(x \right)
F_{63}\! \left(x \right) = F_{36}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{14}\! \left(x \right) F_{36}\! \left(x \right)
F_{66}\! \left(x \right) = F_{60}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 3 F_{32}\! \left(x \right)+F_{68}\! \left(x \right)+F_{72}\! \left(x \right)
F_{68}\! \left(x \right) = F_{14}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{64}\! \left(x \right)
F_{71}\! \left(x \right) = F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{32}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{36}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{55}\! \left(x \right)+F_{73}\! \left(x \right)
F_{78}\! \left(x \right) = F_{14}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{54}\! \left(x \right)+F_{78}\! \left(x \right)
F_{83}\! \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_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{17}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{14}\! \left(x \right) F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{102}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{14}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{46}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{90}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{95}\! \left(x \right)+F_{98}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{52}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{94}\! \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_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{14}\! \left(x \right)
F_{101}\! \left(x \right) = F_{17}\! \left(x \right)+F_{99}\! \left(x \right)
F_{102}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{103}\! \left(x \right)+F_{118}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{14}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{108}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{87}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{14}\! \left(x \right) F_{87}\! \left(x \right)
F_{108}\! \left(x \right) = F_{102}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = 3 F_{32}\! \left(x \right)+F_{110}\! \left(x \right)+F_{114}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{14}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{106}\! \left(x \right)
F_{113}\! \left(x \right) = F_{109}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{14}\! \left(x \right)
F_{115}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{116}\! \left(x \right)+F_{118}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{14}\! \left(x \right)
F_{117}\! \left(x \right) = F_{115}\! \left(x \right)+F_{87}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{14}\! \left(x \right)
F_{119}\! \left(x \right) = F_{115}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_14(x)*F_7(x))
Eq(F_7(x), F_28(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_20(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_12(x) + F_16(x))
Eq(F_16(x), F_17(x)**2)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_14(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_14(x)*F_23(x))
Eq(F_23(x), F_20(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_14(x)*F_26(x))
Eq(F_26(x), F_23(x) + F_27(x))
Eq(F_27(x), F_17(x)*F_19(x))
Eq(F_28(x), F_19(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_83(x))
Eq(F_30(x), F_17(x) + F_31(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_58(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_14(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_42(x))
Eq(F_35(x), F_17(x) + F_36(x))
Eq(F_36(x), F_32(x) + F_37(x) + F_38(x))
Eq(F_37(x), F_14(x)*F_35(x))
Eq(F_38(x), F_14(x)*F_39(x))
Eq(F_39(x), F_14(x) + F_40(x))
Eq(F_40(x), F_32(x) + F_38(x) + F_41(x))
Eq(F_41(x), F_14(x)*F_17(x))
Eq(F_42(x), F_43(x) + F_60(x))
Eq(F_43(x), F_32(x) + F_44(x) + F_58(x))
Eq(F_44(x), F_14(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_48(x))
Eq(F_46(x), F_17(x) + F_47(x))
Eq(F_47(x), F_41(x))
Eq(F_48(x), F_43(x) + F_49(x))
Eq(F_49(x), 2*F_32(x) + F_50(x) + F_54(x))
Eq(F_50(x), F_14(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_47(x))
Eq(F_53(x), F_49(x))
Eq(F_54(x), F_14(x)*F_55(x))
Eq(F_55(x), F_32(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_14(x)*F_57(x))
Eq(F_57(x), F_17(x) + F_55(x))
Eq(F_58(x), F_14(x)*F_59(x))
Eq(F_59(x), F_17(x) + F_55(x))
Eq(F_60(x), F_32(x) + F_61(x) + F_76(x) + F_78(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_66(x))
Eq(F_63(x), F_36(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_14(x)*F_36(x))
Eq(F_66(x), F_60(x) + F_67(x))
Eq(F_67(x), 3*F_32(x) + F_68(x) + F_72(x))
Eq(F_68(x), F_14(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_64(x))
Eq(F_71(x), F_67(x))
Eq(F_72(x), F_14(x)*F_73(x))
Eq(F_73(x), F_32(x) + F_74(x) + F_76(x) + F_78(x))
Eq(F_74(x), F_14(x)*F_75(x))
Eq(F_75(x), F_36(x) + F_73(x))
Eq(F_76(x), F_14(x)*F_77(x))
Eq(F_77(x), F_55(x) + F_73(x))
Eq(F_78(x), F_14(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_82(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_14(x)*F_17(x))
Eq(F_82(x), 2*F_32(x) + F_54(x) + F_78(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_14(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_17(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_14(x)*F_86(x))
Eq(F_89(x), F_102(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_14(x)*F_92(x))
Eq(F_92(x), F_46(x) + F_93(x))
Eq(F_93(x), F_90(x) + F_94(x))
Eq(F_94(x), 2*F_32(x) + F_95(x) + F_98(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_52(x) + F_97(x))
Eq(F_97(x), F_94(x))
Eq(F_98(x), F_14(x)*F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_14(x))
Eq(F_101(x), F_17(x) + F_99(x))
Eq(F_102(x), F_103(x) + F_118(x) + 2*F_32(x))
Eq(F_103(x), F_104(x)*F_14(x))
Eq(F_104(x), F_105(x) + F_108(x))
Eq(F_105(x), F_106(x) + F_87(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_14(x)*F_87(x))
Eq(F_108(x), F_102(x) + F_109(x))
Eq(F_109(x), F_110(x) + F_114(x) + 3*F_32(x))
Eq(F_110(x), F_111(x)*F_14(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_106(x))
Eq(F_113(x), F_109(x))
Eq(F_114(x), F_115(x)*F_14(x))
Eq(F_115(x), F_116(x) + F_118(x) + 2*F_32(x))
Eq(F_116(x), F_117(x)*F_14(x))
Eq(F_117(x), F_115(x) + F_87(x))
Eq(F_118(x), F_119(x)*F_14(x))
Eq(F_119(x), F_115(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, 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