0132_1230_1302
Counting sequence:
1, 1, 2, 6, 21, 74, 253, 840, 2728, 8719, 27541, 86221, 268047, 828661, 2550116, 7818174, 23893803, 72831350, 221504503, 672394824, 2037817846, 6167472211, 18643839127, 56301766021, 169874621301, 512161584769, 1543128593438, 4646779576590, 13985876279193, 42076847689274, 126542662073161, 380445124383456, 1143474668636572, 3436024754203951, 10322737212007921, 31006599735917269, 93120300558035763, 279624017625065125, 839560899377784368, 2520486121690161654, 7566179789238320991, 22710900216661661846, 68165061772657245427, 204579907837041816336, 613961529945663428506, 1842465286621534143139, 5528916143783696021923, 16590728586323824984765, 49782605939970592117833, 149375098207936390924129, 448196715606883899319706, 1344777129381851263029366, 4034820914846077757750397, 12105744342078605614166666, 36320588292156409896582901, 108970549076690636511080664, 326934644564815536943153648, 980864141498456086237862575, 2942750050572653057528879533, 8828662822145804093624110909, 26487068851643662245169456311, 79464035040121891707362265781, 238399510190732140073351362652, 715217917298104910101993885326, 2145704507001673735000536481011, 6437246399601189729203334118934, 19312087079484715755520621557583, 57937172001901418446091997597240, 173813900415364922308955772362398, 521447943711629496659376522872659, 1564360174121832012204977406401551, 4693123308860791873562966526767701, 14079481943081319609306154665206397, 42238739092245494956822194942763681, 126716985049242149268560522584818806, 380152965202241904871059650076892734, 1140464157997766421411219259441456833, 3421406251111905927562400623634267450, 10264254822300497065875390097621711873, 30792858896677222383861992127711964464, 92378823910394081427105253660957467556, 277137118962493755921637770981490293391, 831413051361053388410360065662502975177, 2494243590272565015527098445142987316741, 7482742384912337476823903327177365025691, 22448257560831534870903515708621825909029, 67344852286683529503763356315386267144168, 202034765266522840744016690787631438848390, 606104841414796354039177128697791439372263, 1818315952683600305306185933256593049178614, 5454951597753206813677394384924538217890571, 16364864583927626891120038363074673133670336, 49094619384084494125864844128972435770648322, 147283925258490316285020864297861497940854371, 441851951461879837124836859586668649339650011, 1325556314338629342276407046928314223941297229, 3976670147188448631265136278596783344073842193, 11930013594130037876201257781057563773049026625, 35790049035911628971385405041162491869379625138, 107370168715734740960095261272189663518009006694, 322110562717682269675321290564685753733404864101
Generating function in Maple syntax:
-(7*x^5-22*x^4+33*x^3-24*x^2+8*x-1)/(3*x-1)/(x^2-3*x+1)/(-1+x)^3
Generating function in latex syntax:
-\frac{7 x^{5}-22 x^{4}+33 x^{3}-24 x^{2}+8 x -1}{\left(3 x -1\right) \left(x^{2}-3 x +1\right) \left(-1+x \right)^{3}}
Generating function in sympy syntax:
(-7*x**5 + 22*x**4 - 33*x**3 + 24*x**2 - 8*x + 1)/((x - 1)**3*(3*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(3*x-1)*(x^2-3*x+1)*(-1+x)^3*F(x)+7*x^5-22*x^4+33*x^3-24*x^2+8*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x -1\right) \left(x^{2}-3 x +1\right) \left(-1+x \right)^{3} F \! \left(x \right)+7 x^{5}-22 x^{4}+33 x^{3}-24 x^{2}+8 x -1 = 0
Explicit closed form in Maple syntax:
1/8*(-4*5^(1/2)+4)*(3/2-1/2*5^(1/2))^(-n)+1/8*(4*5^(1/2)+4)*(3/2+1/2*5^(1/2))^(-n)-1/4*n^2+n+5/8*3^n-5/8
Explicit closed form in latex syntax:
\frac{\left(-4 \sqrt{5}+4\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{8}+\frac{\left(4 \sqrt{5}+4\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{8}-\frac{n^{2}}{4}+n +\frac{5 \,3^{n}}{8}-\frac{5}{8}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 74
a(n+3) = -1/2*n^2+3*a(n)-10*a(n+1)+6*a(n+2)+3/2*n+1, 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) = 21
a \! \left(5\right) = 74
a \! \left(n +3\right) = -\frac{n^{2}}{2}+3 a \! \left(n \right)-10 a \! \left(n +1\right)+6 a \! \left(n +2\right)+\frac{3 n}{2}+1, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14723/
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[40,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[26,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[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[12,x]
F[24,x] = F[19,x]
F[25,x] = F[12,x]*F[14,x]
F[26,x] = F[20,x]+F[27,x]+F[39,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[10,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[10,x]*F[12,x]
F[32,x] = F[26,x]+F[33,x]
F[33,x] = 2*F[20,x]+F[34,x]+F[38,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[30,x]
F[37,x] = F[33,x]
F[38,x] = F[12,x]*F[26,x]
F[39,x] = F[12,x]*F[13,x]
F[40,x] = F[41,x]+F[54,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[1,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[44,x]
F[47,x] = F[41,x]+F[48,x]
F[48,x] = F[20,x]+F[49,x]+F[53,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[45,x]
F[52,x] = F[48,x]
F[53,x] = F[12,x]*F[47,x]
F[54,x] = F[20,x]+F[55,x]+F[80,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[57,x]+F[62,x]
F[57,x] = F[58,x]+F[6,x]
F[58,x] = F[59,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[10,x]+F[61,x]
F[61,x] = F[59,x]
F[62,x] = F[54,x]+F[63,x]
F[63,x] = 2*F[20,x]+F[64,x]+F[68,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[58,x]
F[67,x] = F[63,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[70,x]+F[75,x]
F[70,x] = F[20,x]+F[71,x]+F[73,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[60,x]+F[69,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[41,x]+F[70,x]
F[75,x] = 2*F[20,x]+F[68,x]+F[76,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[61,x]
F[79,x] = F[75,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[74,x]+F[82,x]
F[82,x] = F[101,x]+F[83,x]
F[83,x] = F[20,x]+F[49,x]+F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[93,x]
F[86,x] = F[41,x]+F[87,x]
F[87,x] = F[20,x]+F[88,x]+F[92,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[12,x]
F[91,x] = F[87,x]
F[92,x] = F[12,x]*F[41,x]
F[93,x] = F[83,x]+F[94,x]
F[94,x] = F[100,x]+F[20,x]+F[95,x]+F[96,x]
F[95,x] = 0
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[87,x]
F[99,x] = F[94,x]
F[100,x] = F[12,x]*F[83,x]
F[101,x] = F[102,x]+F[119,x]+F[20,x]+F[76,x]
F[102,x] = F[103,x]*F[12,x]
F[103,x] = F[104,x]+F[111,x]
F[104,x] = F[105,x]+F[70,x]
F[105,x] = 2*F[20,x]+F[106,x]+F[110,x]
F[106,x] = F[107,x]*F[12,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[30,x]
F[109,x] = F[105,x]
F[110,x] = F[12,x]*F[70,x]
F[111,x] = F[101,x]+F[112,x]
F[112,x] = 2*F[20,x]+F[113,x]+F[114,x]+F[118,x]
F[113,x] = 0
F[114,x] = F[115,x]*F[12,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[105,x]
F[117,x] = F[112,x]
F[118,x] = F[101,x]*F[12,x]
F[119,x] = F[12,x]*F[82,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_{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_{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_{26}\! \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_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)+F_{39}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{10}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{34}\! \left(x \right)+F_{38}\! \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_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{54}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{41}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{20}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{45}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{54}\! \left(x \right) = F_{20}\! \left(x \right)+F_{55}\! \left(x \right)+F_{80}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{62}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{6}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{10}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{54}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{58}\! \left(x \right)
F_{67}\! \left(x \right) = F_{63}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{75}\! \left(x \right)
F_{70}\! \left(x \right) = F_{20}\! \left(x \right)+F_{71}\! \left(x \right)+F_{73}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{60}\! \left(x \right)+F_{69}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{41}\! \left(x \right)+F_{70}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{68}\! \left(x \right)+F_{76}\! \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_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{61}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{74}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{101}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{20}\! \left(x \right)+F_{49}\! \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_{86}\! \left(x \right)+F_{93}\! \left(x \right)
F_{86}\! \left(x \right) = F_{41}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right)+F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right)
F_{91}\! \left(x \right) = F_{87}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{93}\! \left(x \right) = F_{83}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{100}\! \left(x \right)+F_{20}\! \left(x \right)+F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = 0
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{87}\! \left(x \right)
F_{99}\! \left(x \right) = F_{94}\! \left(x \right)
F_{100}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{119}\! \left(x \right)+F_{20}\! \left(x \right)+F_{76}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{111}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{70}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{106}\! \left(x \right)+F_{110}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{12}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{30}\! \left(x \right)
F_{109}\! \left(x \right) = F_{105}\! \left(x \right)
F_{110}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{111}\! \left(x \right) = F_{101}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{113}\! \left(x \right)+F_{114}\! \left(x \right)+F_{118}\! \left(x \right)
F_{113}\! \left(x \right) = 0
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{105}\! \left(x \right)
F_{117}\! \left(x \right) = F_{112}\! \left(x \right)
F_{118}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \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_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_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_26(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) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_12(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_12(x)*F_14(x))
Eq(F_26(x), F_20(x) + F_27(x) + F_39(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_10(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_10(x)*F_12(x))
Eq(F_32(x), F_26(x) + F_33(x))
Eq(F_33(x), 2*F_20(x) + F_34(x) + F_38(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_33(x))
Eq(F_38(x), F_12(x)*F_26(x))
Eq(F_39(x), F_12(x)*F_13(x))
Eq(F_40(x), F_41(x) + F_54(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_1(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_44(x))
Eq(F_47(x), F_41(x) + F_48(x))
Eq(F_48(x), F_20(x) + F_49(x) + F_53(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_45(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_12(x)*F_47(x))
Eq(F_54(x), F_20(x) + F_55(x) + F_80(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_62(x))
Eq(F_57(x), F_58(x) + F_6(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_10(x) + F_61(x))
Eq(F_61(x), F_59(x))
Eq(F_62(x), F_54(x) + F_63(x))
Eq(F_63(x), 2*F_20(x) + F_64(x) + F_68(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_58(x))
Eq(F_67(x), F_63(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_75(x))
Eq(F_70(x), F_20(x) + F_71(x) + F_73(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_60(x) + F_69(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_41(x) + F_70(x))
Eq(F_75(x), 2*F_20(x) + F_68(x) + F_76(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_61(x))
Eq(F_79(x), F_75(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_74(x) + F_82(x))
Eq(F_82(x), F_101(x) + F_83(x))
Eq(F_83(x), F_20(x) + F_49(x) + F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_93(x))
Eq(F_86(x), F_41(x) + F_87(x))
Eq(F_87(x), F_20(x) + F_88(x) + F_92(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_12(x))
Eq(F_91(x), F_87(x))
Eq(F_92(x), F_12(x)*F_41(x))
Eq(F_93(x), F_83(x) + F_94(x))
Eq(F_94(x), F_100(x) + F_20(x) + F_95(x) + F_96(x))
Eq(F_95(x), 0)
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_87(x))
Eq(F_99(x), F_94(x))
Eq(F_100(x), F_12(x)*F_83(x))
Eq(F_101(x), F_102(x) + F_119(x) + F_20(x) + F_76(x))
Eq(F_102(x), F_103(x)*F_12(x))
Eq(F_103(x), F_104(x) + F_111(x))
Eq(F_104(x), F_105(x) + F_70(x))
Eq(F_105(x), F_106(x) + F_110(x) + 2*F_20(x))
Eq(F_106(x), F_107(x)*F_12(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_30(x))
Eq(F_109(x), F_105(x))
Eq(F_110(x), F_12(x)*F_70(x))
Eq(F_111(x), F_101(x) + F_112(x))
Eq(F_112(x), F_113(x) + F_114(x) + F_118(x) + 2*F_20(x))
Eq(F_113(x), 0)
Eq(F_114(x), F_115(x)*F_12(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_105(x))
Eq(F_117(x), F_112(x))
Eq(F_118(x), F_101(x)*F_12(x))
Eq(F_119(x), F_12(x)*F_82(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": [1, 3, 0, 2], "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": [1, 3, 0, 2], "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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 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": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 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": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 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": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 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]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 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": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 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": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 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]]}], "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]]}], "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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 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": [[0, 0], [0, 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