0213_0321_2130
Counting sequence:
1, 1, 2, 6, 21, 74, 249, 797, 2451, 7318, 21380, 61449, 174378, 489827, 1364499, 3774779, 10381722, 28410568, 77414615, 210156558, 568645563, 1534219643, 4128788739, 11085822020, 29704820778, 79449163033, 212145068252, 565621458225, 1506010540935, 4004905219913, 10638135417084, 28228620651332, 74834538691485, 198214936836292, 524593335557183, 1387358054192301, 3666557269988445, 9684003797082092, 25562211024721572, 67438436013298475, 177827609566645728, 468693679921838179, 1234785436590954869, 3251767756897788945, 8560226172034630146, 22526814494877419810, 59261605946762099205, 155853164217506820446, 409765298230341738045, 1077060738113855593897, 2830337371665950792843, 7435945395474963908118, 19531726634270192280096, 51292937059089959956673, 134676737708233720315470, 353550059426309350815167, 927977415842579808877527, 2435323131881183331856891, 6390174228642650276589866, 16765235756330378007544692, 43979589436613785103206983, 115356123873679170452257586, 302538974090620823597373183, 793370778610926628035673271, 2080310097022651464024398811, 5454307128233872031648897572, 14299248015022109666881464566, 37484455953162292985319563265, 98255255200398920977411763712, 257530666072151331726511058093, 674951549041841270927802240459, 1768839829103735414126645947193, 4635305369614236305441518577964, 12146291182944002762983732764208, 31826288179464621155915307592205, 83388591134446725092423735565576, 218477601048243853592331410862003, 572384746413514259147381699917145, 1499516250020365713509165578348389, 3928234126416807821116393113752732, 10290290164376311830876800238804000, 26955220728935219665957818781489363, 70606399663898119558796802677387636, 184940479122957530848524479071099839, 484403656025093454363474894495489609, 1268735540856213115733634234866719073, 3322949585139107295435148301573458194, 8702940284384259907634117263350800606, 22792841610040140813203029496477621349, 59692770420512964597399903764997420610, 156327842649943072723204201694674115825, 409395231175288927379125596233082075573, 1072115438091923212117061364796749400515, 2807586182729948309981671694444067966950, 7352208993473712629772701299464346862268, 19252901594695013730176022879606564731561, 50416014860636073407418831726201959492514, 132018612932420437860370619210884478913643, 345697690758341913866055063646731853453691, 905217134113510076205782381291546596910523, 2370305486392845730266303570511103613606858
Generating function in Maple syntax:
-(5*x^5-19*x^4+25*x^3-19*x^2+7*x-1)/(x-1)/(x^2-3*x+1)/(3*x^3-5*x^2+4*x-1)
Generating function in latex syntax:
-\frac{5 x^{5}-19 x^{4}+25 x^{3}-19 x^{2}+7 x -1}{\left(x -1\right) \left(x^{2}-3 x +1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right)}
Generating function in sympy syntax:
(-5*x**5 + 19*x**4 - 25*x**3 + 19*x**2 - 7*x + 1)/((x - 1)*(x**2 - 3*x + 1)*(3*x**3 - 5*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^2-3*x+1)*(3*x^3-5*x^2+4*x-1)*F(x)+5*x^5-19*x^4+25*x^3-19*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{2}-3 x +1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) F \! \left(x \right)+5 x^{5}-19 x^{4}+25 x^{3}-19 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
1/450120*(6820*((-129/62*I+43/62*3^(1/2))*31^(1/2)+I*3^(1/2)-1)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3)-750200+15035*2^(1/3)*((-399/3007*I-133/3007*3^(1/2))*31^(1/2)+I*3^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(2/3))*(47/8712*((I-9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)+1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/450120*(-6820*((-129/62*I-43/62*3^(1/2))*31^(1/2)+I*3^(1/2)+1)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3)-750200-15035*2^(1/3)*((-399/3007*I+133/3007*3^(1/2))*31^(1/2)+I*3^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(2/3))*(-47/8712*((I+9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)-1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3)+1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/450120*((-9460*3^(1/2)*2^(2/3)*31^(1/2)+13640*2^(2/3))*(47+9*31^(1/2)*3^(1/2))^(1/3)-750200+(1330*31^(1/2)*3^(1/2)*2^(1/3)-30070*2^(1/3))*(47+9*31^(1/2)*3^(1/2))^(2/3))*(1/4356*2^(1/3)*(9*31^(1/2)*3^(1/2)-47)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/18*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/450120*(360096*5^(1/2)+900240)*(3/2-1/2*5^(1/2))^(-n)+2+1/450120*(-360096*5^(1/2)+900240)*(3/2+1/2*5^(1/2))^(-n)
Explicit closed form in latex syntax:
\frac{\left(6820 \left(\left(-\frac{129 \,\mathrm{I}}{62}+\frac{43 \sqrt{3}}{62}\right) \sqrt{31}+\mathrm{I} \sqrt{3}-1\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-750200+15035 \,2^{\frac{1}{3}} \left(\left(-\frac{399 \,\mathrm{I}}{3007}-\frac{133 \sqrt{3}}{3007}\right) \sqrt{31}+\mathrm{I} \sqrt{3}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{47 \left(\left(\mathrm{I}-\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}+1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}-\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{450120}+\frac{\left(-6820 \left(\left(-\frac{129 \,\mathrm{I}}{62}-\frac{43 \sqrt{3}}{62}\right) \sqrt{31}+\mathrm{I} \sqrt{3}+1\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-750200-15035 \,2^{\frac{1}{3}} \left(\left(-\frac{399 \,\mathrm{I}}{3007}+\frac{133 \sqrt{3}}{3007}\right) \sqrt{31}+\mathrm{I} \sqrt{3}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{47 \left(\left(\mathrm{I}+\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}-1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}+\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{450120}+\frac{\left(\left(-9460 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{31}+13640 \,2^{\frac{2}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-750200+\left(1330 \sqrt{31}\, \sqrt{3}\, 2^{\frac{1}{3}}-30070 \,2^{\frac{1}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(9 \sqrt{31}\, \sqrt{3}-47\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{4356}-\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{18}+\frac{5}{9}\right)^{-n}}{450120}+\frac{\left(360096 \sqrt{5}+900240\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{450120}+2+\frac{\left(-360096 \sqrt{5}+900240\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{450120}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 74
a(n+5) = 3*a(n)-14*a(n+1)+22*a(n+2)-18*a(n+3)+7*a(n+4)+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) = 21
a \! \left(5\right) = 74
a \! \left(n +5\right) = 3 a \! \left(n \right)-14 a \! \left(n +1\right)+22 a \! \left(n +2\right)-18 a \! \left(n +3\right)+7 a \! \left(n +4\right)+2, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14748/
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[17,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[5,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[13,x]
F[12,x] = x
F[13,x] = F[1,x]+F[10,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[9,x]
F[17,x] = F[18,x]+F[32,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[21,x]+F[5,x]
F[21,x] = F[18,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[21,x]+F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[27,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[18,x]+F[26,x]
F[29,x] = F[30,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[25,x]
F[32,x] = F[33,x]+F[34,x]+F[75,x]
F[33,x] = 0
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[53,x]
F[36,x] = F[37,x]+F[6,x]
F[37,x] = F[33,x]+F[38,x]+F[44,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[36,x]+F[40,x]
F[40,x] = F[14,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[40,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[46,x]+F[9,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[48,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[10,x]+F[47,x]
F[50,x] = F[51,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[46,x]
F[53,x] = F[32,x]+F[54,x]
F[54,x] = 2*F[33,x]+F[55,x]+F[65,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[53,x]+F[57,x]
F[57,x] = F[58,x]+F[62,x]
F[58,x] = F[59,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[26,x]+F[58,x]
F[62,x] = F[63,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[57,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[61,x]+F[67,x]
F[67,x] = F[68,x]+F[72,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[26,x]+F[71,x]
F[71,x] = F[69,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[67,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[17,x]+F[77,x]
F[77,x] = F[103,x]+F[78,x]
F[78,x] = F[27,x]+F[33,x]+F[79,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]+F[92,x]
F[81,x] = F[10,x]+F[82,x]
F[82,x] = F[33,x]+F[83,x]+F[87,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[81,x]+F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[10,x]+F[86,x]
F[89,x] = F[90,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[85,x]
F[92,x] = F[26,x]+F[93,x]
F[93,x] = 2*F[33,x]+F[94,x]+F[98,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[92,x]+F[96,x]
F[96,x] = F[100,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[26,x]+F[97,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[96,x]
F[103,x] = 2*F[33,x]+F[104,x]+F[122,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[106,x]+F[112,x]
F[106,x] = F[107,x]+F[14,x]
F[107,x] = 2*F[33,x]+F[108,x]+F[110,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[106,x]
F[110,x] = F[111,x]*F[12,x]
F[111,x] = F[46,x]
F[112,x] = F[113,x]+F[58,x]
F[113,x] = 3*F[33,x]+F[114,x]+F[116,x]
F[114,x] = F[115,x]*F[12,x]
F[115,x] = F[112,x]
F[116,x] = F[117,x]*F[12,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]+F[71,x]
F[119,x] = F[120,x]
F[120,x] = F[12,x]*F[121,x]
F[121,x] = F[118,x]
F[122,x] = F[12,x]*F[123,x]
F[123,x] = F[77,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_{17}\! \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_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \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_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{32}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{5}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{75}\! \left(x \right)
F_{33}\! \left(x \right) = 0
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_{53}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{6}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right)+F_{41}\! \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_{40}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{9}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{10}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)
F_{53}\! \left(x \right) = F_{32}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{55}\! \left(x \right)+F_{65}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{62}\! \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_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{26}\! \left(x \right)+F_{58}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{57}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{61}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{72}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{26}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{67}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{17}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{103}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{92}\! \left(x \right)
F_{81}\! \left(x \right) = F_{10}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{33}\! \left(x \right)+F_{83}\! \left(x \right)+F_{87}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{81}\! \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_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{10}\! \left(x \right)+F_{86}\! \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_{85}\! \left(x \right)
F_{92}\! \left(x \right) = F_{26}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{94}\! \left(x \right)+F_{98}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{100}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{26}\! \left(x \right)+F_{97}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{96}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{104}\! \left(x \right)+F_{122}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{112}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{14}\! \left(x \right)
F_{107}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{108}\! \left(x \right)+F_{110}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{106}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{12}\! \left(x \right)
F_{111}\! \left(x \right) = F_{46}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{58}\! \left(x \right)
F_{113}\! \left(x \right) = 3 F_{33}\! \left(x \right)+F_{114}\! \left(x \right)+F_{116}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{112}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{71}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{118}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{77}\! \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_17(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_5(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_13(x))
Eq(F_12(x), x)
Eq(F_13(x), F_1(x) + F_10(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_9(x))
Eq(F_17(x), F_18(x) + F_32(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_5(x))
Eq(F_21(x), F_18(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_21(x) + F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_18(x) + F_26(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_25(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_75(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_53(x))
Eq(F_36(x), F_37(x) + F_6(x))
Eq(F_37(x), F_33(x) + F_38(x) + F_44(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_36(x) + F_40(x))
Eq(F_40(x), F_14(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_40(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_9(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_10(x) + F_47(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_46(x))
Eq(F_53(x), F_32(x) + F_54(x))
Eq(F_54(x), 2*F_33(x) + F_55(x) + F_65(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_53(x) + F_57(x))
Eq(F_57(x), F_58(x) + F_62(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_26(x) + F_58(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_57(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_61(x) + F_67(x))
Eq(F_67(x), F_68(x) + F_72(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_26(x) + F_71(x))
Eq(F_71(x), F_69(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_67(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_17(x) + F_77(x))
Eq(F_77(x), F_103(x) + F_78(x))
Eq(F_78(x), F_27(x) + F_33(x) + F_79(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_92(x))
Eq(F_81(x), F_10(x) + F_82(x))
Eq(F_82(x), F_33(x) + F_83(x) + F_87(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_81(x) + F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_10(x) + F_86(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_85(x))
Eq(F_92(x), F_26(x) + F_93(x))
Eq(F_93(x), 2*F_33(x) + F_94(x) + F_98(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_92(x) + F_96(x))
Eq(F_96(x), F_100(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_26(x) + F_97(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_96(x))
Eq(F_103(x), F_104(x) + F_122(x) + 2*F_33(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_106(x) + F_112(x))
Eq(F_106(x), F_107(x) + F_14(x))
Eq(F_107(x), F_108(x) + F_110(x) + 2*F_33(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_106(x))
Eq(F_110(x), F_111(x)*F_12(x))
Eq(F_111(x), F_46(x))
Eq(F_112(x), F_113(x) + F_58(x))
Eq(F_113(x), F_114(x) + F_116(x) + 3*F_33(x))
Eq(F_114(x), F_115(x)*F_12(x))
Eq(F_115(x), F_112(x))
Eq(F_116(x), F_117(x)*F_12(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x) + F_71(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_12(x)*F_121(x))
Eq(F_121(x), F_118(x))
Eq(F_122(x), F_12(x)*F_123(x))
Eq(F_123(x), F_77(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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "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": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 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