0132_0213_0321_1230_2130
Counting sequence:
1, 1, 2, 6, 19, 53, 135, 330, 790, 1875, 4442, 10536, 25051, 59723, 142739, 341880, 820290, 1970925, 4740794, 11413106, 27494363, 66268041, 159784167, 385383182, 929716742, 2243282831, 5413460962, 13065015012, 31533945235, 76115347759, 183732346691, 443520642700, 1070664380898, 2584648459769, 6239591704978, 15063152077182, 36364645525379, 87790143404669, 211940702483559, 511663768461938, 1235253929921622, 2982145309056747, 7199496139389322, 17381048550453568, 41961429475018539, 101303606289183155, 244568088039415571, 590438763377457472, 1425443740578494690, 3441322797314082597, 8308082994779900554, 20057477125010921770, 48423015795291655947, 116903469263794421521, 282229881759707633927, 681363099318726921078, 1644955834917706027526, 3971274317647027891047, 9587503639760712504402, 23146280069730837057596, 55880060969826610383523, 134906396842099616437463, 325692845149908009789187, 786292069661117584919444, 1898276952319942853671234, 4582845915163887081735281, 11063968673877602429557666, 26710783062859660816778614, 64485534431630262140927603, 155681851249323977464785733, 375849235685455916390386887, 907380320330650640009407002, 2190609872135553517859083030, 5288600056856146526261185283, 12767809971601446572128790074, 30824219973855824844249590744, 74416249871117870286639739899, 179656719627446724619018994843, 433729688962968037925910241555, 1047116097253499452099573676424, 2527961882918395471356514222850, 6103039862075792294074025454557, 14734041605204027139626179284698, 35571123069051824081940878130786, 85876287736995201791505467131323, 207323698531431778741685452230937, 500523684778503814348222037115303, 1208371068049161540076206363398750, 2917265820804583633288790906201990, 7042902709525452733153366820543423, 17003071239611091897521336171247938, 41049045188298119991409585574020116, 99101161615380542067979443998960435, 239251368417538500576146768286544639, 577603898447660533319903758377297731, 1394459165307715063952002294240655132, 3366522229053628444508365428577965602, 8127503623397568223088869020120697705, 19621529475816754440826744428462335538, 47370562574972200708287591787131802606, 114362654625652865281207938741179450595
Generating function in Maple syntax:
-(x^8+4*x^7-x^6-7*x^5-x^4-2*x^3+8*x^2-5*x+1)/(x^2+2*x-1)/(x^3+x^2+x-1)/(x-1)^3
Generating function in latex syntax:
-\frac{x^{8}+4 x^{7}-x^{6}-7 x^{5}-x^{4}-2 x^{3}+8 x^{2}-5 x +1}{\left(x^{2}+2 x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-x**8 - 4*x**7 + x**6 + 7*x**5 + x**4 + 2*x**3 - 8*x**2 + 5*x - 1)/((x - 1)**3*(x**2 + 2*x - 1)*(x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2+2*x-1)*(x^3+x^2+x-1)*(x-1)^3*F(x)+x^8+4*x^7-x^6-7*x^5-x^4-2*x^3+8*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}+2 x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{8}+4 x^{7}-x^{6}-7 x^{5}-x^{4}-2 x^{3}+8 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/1056*(((-36*11^(1/2)+176*I)*3^(1/2)-108*I*11^(1/2)+176)*(17+3*11^(1/2)*3^(1/2))^(1/3)+352+((143*I+21*11^(1/2))*3^(1/2)-63*I*11^(1/2)-143)*(17+3*11^(1/2)*3^(1/2))^(2/3))*(1/24*((17*I+3*11^(1/2))*3^(1/2)-9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/1056*(((-143*I+21*11^(1/2))*3^(1/2)+63*I*11^(1/2)-143)*(17+3*11^(1/2)*3^(1/2))^(2/3)+352+((-176*I-36*11^(1/2))*3^(1/2)+108*I*11^(1/2)+176)*(17+3*11^(1/2)*3^(1/2))^(1/3))*(1/24*((-17*I+3*11^(1/2))*3^(1/2)+9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/1056*((-42*11^(1/2)*3^(1/2)+286)*(17+3*11^(1/2)*3^(1/2))^(2/3)+72*(17+3*11^(1/2)*3^(1/2))^(1/3)*11^(1/2)*3^(1/2)-352*(17+3*11^(1/2)*3^(1/2))^(1/3)+352)*(1/3*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3+17/12*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/4*(17+3*11^(1/2)*3^(1/2))^(2/3)*11^(1/2)*3^(1/2))^(-n)+1/1056*(-264*2^(1/2)+264)*(-1-2^(1/2))^(-n)+1/1056*(264*2^(1/2)+264)*(2^(1/2)-1)^(-n)-1/4*n^2-9/4*n+1/2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(\left(-36 \sqrt{11}+176 \,\mathrm{I}\right) \sqrt{3}-108 \,\mathrm{I} \sqrt{11}+176\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+352+\left(\left(143 \,\mathrm{I}+21 \sqrt{11}\right) \sqrt{3}-63 \,\mathrm{I} \sqrt{11}-143\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}-\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{1056}\\+\\\frac{\left(\left(\left(-143 \,\mathrm{I}+21 \sqrt{11}\right) \sqrt{3}+63 \,\mathrm{I} \sqrt{11}-143\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+352+\left(\left(-176 \,\mathrm{I}-36 \sqrt{11}\right) \sqrt{3}+108 \,\mathrm{I} \sqrt{11}+176\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}+\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{1056}\\+\\\frac{\left(\left(-42 \sqrt{11}\, \sqrt{3}+286\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+72 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{11}\, \sqrt{3}-352 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+352\right) \left(\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}-\frac{1}{3}+\frac{17 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{12}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{11}\, \sqrt{3}}{4}\right)^{-n}}{1056}\\+\frac{\left(-264 \sqrt{2}+264\right) \left(-1-\sqrt{2}\right)^{-n}}{1056}+\frac{\left(264 \sqrt{2}+264\right) \left(\sqrt{2}-1\right)^{-n}}{1056}-\frac{n^{2}}{4}\\-\frac{9 n}{4}+\frac{1}{2} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 53
a(6) = 135
a(7) = 330
a(8) = 790
a(n+2) = -1/2*n^2+3/2*a(n+4)-1/2*a(n+5)-1/2*a(n)-3/2*a(n+1)-9/2*n+5/2, n >= 9
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) = 19
a \! \left(5\right) = 53
a \! \left(6\right) = 135
a \! \left(7\right) = 330
a \! \left(8\right) = 790
a \! \left(n +2\right) = -\frac{n^{2}}{2}+\frac{3 a \! \left(n +4\right)}{2}-\frac{a \! \left(n +5\right)}{2}-\frac{a \! \left(n \right)}{2}-\frac{3 a \! \left(n +1\right)}{2}-\frac{9 n}{2}+\frac{5}{2}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18263/
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[19,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[12,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[32,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[16,x]
F[26,x] = F[20,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[20,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[12,x]*F[20,x]
F[32,x] = F[33,x]+F[34,x]+F[73,x]
F[33,x] = 0
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[50,x]
F[36,x] = F[37,x]+F[6,x]
F[37,x] = F[33,x]+F[38,x]+F[43,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[10,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[12,x]+F[40,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[42,x]+F[45,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[47,x]
F[47,x] = x^2
F[48,x] = F[49,x]
F[49,x] = F[12,x]*F[45,x]
F[50,x] = F[32,x]+F[51,x]
F[51,x] = 2*F[33,x]+F[52,x]+F[66,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[63,x]
F[54,x] = F[33,x]+F[55,x]+F[64,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[57,x]+F[59,x]
F[57,x] = F[10,x]+F[58,x]
F[58,x] = F[33,x]+F[38,x]+F[41,x]
F[59,x] = F[54,x]+F[60,x]
F[60,x] = 2*F[33,x]+F[52,x]+F[61,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[30,x]+F[63,x]
F[63,x] = F[61,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[20,x]+F[54,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[62,x]+F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[70,x]
F[70,x] = F[12,x]*F[30,x]
F[71,x] = F[72,x]
F[72,x] = F[12,x]*F[68,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[65,x]+F[75,x]
F[75,x] = F[76,x]+F[86,x]
F[76,x] = F[33,x]+F[77,x]+F[85,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[12,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = x^2
F[82,x] = F[30,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[12,x]*F[30,x]
F[85,x] = F[12,x]*F[29,x]
F[86,x] = 2*F[33,x]+F[87,x]+F[91,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[40,x]
F[90,x] = F[63,x]
F[91,x] = F[12,x]*F[75,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_{19}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{32}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
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_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{20}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{73}\! \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_{50}\! \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_{43}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{42}\! \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_{47}\! \left(x \right)
F_{47}\! \left(x \right) = x^{2}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{50}\! \left(x \right) = F_{32}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{52}\! \left(x \right)+F_{66}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{63}\! \left(x \right)
F_{54}\! \left(x \right) = F_{33}\! \left(x \right)+F_{55}\! \left(x \right)+F_{64}\! \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_{59}\! \left(x \right)
F_{57}\! \left(x \right) = F_{10}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{59}\! \left(x \right) = F_{54}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{52}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{30}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{20}\! \left(x \right)+F_{54}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{62}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{65}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{86}\! \left(x \right)
F_{76}\! \left(x \right) = F_{33}\! \left(x \right)+F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \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_{81}\! \left(x \right) = x^{2}
F_{82}\! \left(x \right) = F_{30}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{87}\! \left(x \right)+F_{91}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{40}\! \left(x \right)
F_{90}\! \left(x \right) = F_{63}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \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_19(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_12(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_13(x))
Eq(F_19(x), F_20(x) + F_32(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_16(x))
Eq(F_26(x), F_20(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_20(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_12(x)*F_20(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_73(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_50(x))
Eq(F_36(x), F_37(x) + F_6(x))
Eq(F_37(x), F_33(x) + F_38(x) + F_43(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_10(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_12(x) + F_40(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_42(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_48(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), x**2)
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_12(x)*F_45(x))
Eq(F_50(x), F_32(x) + F_51(x))
Eq(F_51(x), 2*F_33(x) + F_52(x) + F_66(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_63(x))
Eq(F_54(x), F_33(x) + F_55(x) + F_64(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_59(x))
Eq(F_57(x), F_10(x) + F_58(x))
Eq(F_58(x), F_33(x) + F_38(x) + F_41(x))
Eq(F_59(x), F_54(x) + F_60(x))
Eq(F_60(x), 2*F_33(x) + F_52(x) + F_61(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_30(x) + F_63(x))
Eq(F_63(x), F_61(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_20(x) + F_54(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_62(x) + F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_12(x)*F_30(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_12(x)*F_68(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_65(x) + F_75(x))
Eq(F_75(x), F_76(x) + F_86(x))
Eq(F_76(x), F_33(x) + F_77(x) + F_85(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_12(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), x**2)
Eq(F_82(x), F_30(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_12(x)*F_30(x))
Eq(F_85(x), F_12(x)*F_29(x))
Eq(F_86(x), 2*F_33(x) + F_87(x) + F_91(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_40(x))
Eq(F_90(x), F_63(x))
Eq(F_91(x), F_12(x)*F_75(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": [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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "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": [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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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": [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": [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": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 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": [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": [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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "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": [[1, 0], [1, 0], [1, 0]]}, {"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, 1, 3, 2], "pos": [[0, 0], [0, 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": [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": [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": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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": [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": [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": []}, "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, 0, 2], "pos": [[0, 0], [0, 0], [0, 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