0123_0213_1032
Counting sequence:
1, 1, 2, 6, 21, 75, 268, 958, 3425, 12245, 43778, 156514, 559565, 2000543, 7152292, 25570698, 91419729, 326841561, 1168515890, 4177649198, 14935828405, 53398205443, 190907947468, 682529386598, 2440162233937, 8724007852045, 31189857766034, 111509210441322, 398664979703373, 1425297205610871, 5095687426153348, 18217976042357074, 65132458748639969, 232859960556541553, 832515189387447074, 2976387777891628054, 10641108195156061205, 38043827643059341307, 136013354548321051852, 486271591519586019150, 1738506204072664594305, 6215464514705069101317, 22221375479165798203106, 79445313703878797779250, 284030926682521068319117, 1015460365765953205022863, 3630448861627362480808612, 12979491254638706852047706, 46403957100149487788300209, 165902283248809309205699785, 593129752442588312469485522, 2120542866218394900191095230, 7581312569385872106448509237, 27104521766743065941145117747, 96903417908194721039596157452, 346446710371846101588800317558, 1238607736635095224051850681585, 4428239839846335069167849288381, 15831733888950647310705700268018, 56601224639008263451002003540922, 202359302721189334096880461522829, 723469989544795769037761390257127, 2586532068125870287548582944796676, 9247305674217260016861567918177186, 33060739236985701696327748102106817, 118197939746215231557647261071409121, 422578359791198172584108100972980546, 1510791732472116370596931810035140390, 5401345350561513898638477812235311893, 19310756717138003966970616569745518763, 69039341272582022639215266173608751500, 246827750624702994049599855369379451870, 882452488037362424955271644457556030113, 3154922376728069753033346782868937200949, 11279400690814378127682828287125786895810, 40325835235251394860525563016311005789698, 144171931824795600267848017412272767738957, 515439935833580297852673253407851695967103, 1842788149464418402468365276552357473074084, 6588290754604852819843285071201961030050346, 23554294659332939469873908221106559798248465, 84210733491217308746893120041719180383074233, 301068138005948643285042868590515166522826610, 1076371383605420981766289765649633463891604558, 3848216430732888318518985657279835323488665013, 13758048498241391288366555714959385518834029923, 49187435760704681836675788207986623189619172172, 175853707524196300425241722950937758903894354310, 628707839141125732285829441160416724950518467729, 2247740764539278300677819339440805242854689476717, 8036067359162549657153426133136276416135890507858, 28730349878329697191404483013033390869831325659146, 102716038484931120320380889023582204407812382106573, 367227848136850907912343622995093783481003968646999, 1312903947975038235734268253826141230431917871185284, 4693861822717983670561743064348508372711456986001138, 16781379052710628906282742106708356392536187756821409, 59996372613219773847563675182793597502104668829006929, 214497552044918766683078434392628552738337295903201890, 766866359235938793179190128353995220361500764482435382, 2741681699027646558139448252889602614581001616024530197
Generating function in Maple syntax:
-(2*x^3+3*x-1)/(x^4-2*x^3+2*x^2-4*x+1)
Generating function in latex syntax:
-\frac{2 x^{3}+3 x -1}{x^{4}-2 x^{3}+2 x^{2}-4 x +1}
Generating function in sympy syntax:
(-2*x**3 - 3*x + 1)/(x**4 - 2*x**3 + 2*x**2 - 4*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^4-2*x^3+2*x^2-4*x+1)*F(x)+2*x^3+3*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{4}-2 x^{3}+2 x^{2}-4 x +1\right) F \! \left(x \right)+2 x^{3}+3 x -1 = 0
Explicit closed form in Maple syntax:
23/114*Sum(_alpha^(-n+2),_alpha = RootOf(_Z^4-2*_Z^3+2*_Z^2-4*_Z+1))+1/114*Sum(_alpha^(-n+1),_alpha = RootOf(_Z^4-2*_Z^3+2*_Z^2-4*_Z+1))+17/57*Sum(_alpha^(-n),_alpha = RootOf(_Z^4-2*_Z^3+2*_Z^2-4*_Z+1))-1/19*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^4-2*_Z^3+2*_Z^2-4*_Z+1))
Explicit closed form in latex syntax:
\frac{23 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{114}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{114}+\frac{17 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{57}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{19}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+4) = -a(n)+2*a(n+1)-2*a(n+2)+4*a(n+3), n >= 4
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(n +4\right) = -a \! \left(n \right)+2 a \! \left(n +1\right)-2 a \! \left(n +2\right)+4 a \! \left(n +3\right), \quad n \geq 4
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14631/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[16,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[4,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[18,x]+F[19,x]+F[93,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[38,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[1,x]+F[4,x]
F[25,x] = F[18,x]+F[26,x]+F[36,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[29,x]+F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[4,x]
F[31,x] = F[32,x]+F[34,x]
F[32,x] = F[33,x]
F[33,x] = F[4,x]*F[7,x]
F[34,x] = F[35,x]
F[35,x] = F[14,x]*F[4,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[32,x]+F[7,x]
F[38,x] = F[39,x]+F[82,x]
F[39,x] = F[18,x]+F[19,x]+F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[2,x]+F[42,x]
F[42,x] = F[18,x]+F[43,x]+F[81,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[47,x]
F[45,x] = F[4,x]+F[46,x]
F[46,x] = F[18,x]+F[26,x]+F[33,x]
F[47,x] = F[42,x]+F[48,x]
F[48,x] = F[18,x]+F[49,x]+F[66,x]+F[67,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[58,x]
F[51,x] = F[52,x]+F[55,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[4,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[32,x]
F[58,x] = F[59,x]+F[62,x]
F[59,x] = 2*F[18,x]+F[49,x]+F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[42,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[17,x]*F[4,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[75,x]
F[69,x] = F[42,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[18,x]+F[43,x]+F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[2,x]+F[72,x]
F[75,x] = F[65,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[17,x]+F[78,x]
F[81,x] = F[2,x]*F[4,x]
F[82,x] = F[18,x]+F[67,x]+F[83,x]+F[91,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[53,x]
F[87,x] = F[56,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = 2*F[18,x]+F[60,x]+F[83,x]
F[90,x] = F[63,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[17,x]+F[65,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[74,x]+F[80,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{16}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{93}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{38}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \left(x \right)+F_{36}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{32}\! \left(x \right)+F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{82}\! \left(x \right)
F_{39}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{18}\! \left(x \right)+F_{43}\! \left(x \right)+F_{81}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{47}\! \left(x \right) = F_{42}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)+F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{58}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{55}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{32}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{62}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{49}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{42}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{69}\! \left(x \right) = F_{42}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{18}\! \left(x \right)+F_{43}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{65}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{17}\! \left(x \right)+F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{82}\! \left(x \right) = F_{18}\! \left(x \right)+F_{67}\! \left(x \right)+F_{83}\! \left(x \right)+F_{91}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{53}\! \left(x \right)
F_{87}\! \left(x \right) = F_{56}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{83}\! \left(x \right)
F_{90}\! \left(x \right) = F_{63}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{17}\! \left(x \right)+F_{65}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{74}\! \left(x \right)+F_{80}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_16(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_93(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_38(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_1(x) + F_4(x))
Eq(F_25(x), F_18(x) + F_26(x) + F_36(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_29(x) + F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_34(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_4(x)*F_7(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_14(x)*F_4(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_32(x) + F_7(x))
Eq(F_38(x), F_39(x) + F_82(x))
Eq(F_39(x), F_18(x) + F_19(x) + F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_2(x) + F_42(x))
Eq(F_42(x), F_18(x) + F_43(x) + F_81(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_47(x))
Eq(F_45(x), F_4(x) + F_46(x))
Eq(F_46(x), F_18(x) + F_26(x) + F_33(x))
Eq(F_47(x), F_42(x) + F_48(x))
Eq(F_48(x), F_18(x) + F_49(x) + F_66(x) + F_67(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_58(x))
Eq(F_51(x), F_52(x) + F_55(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_4(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_32(x))
Eq(F_58(x), F_59(x) + F_62(x))
Eq(F_59(x), 2*F_18(x) + F_49(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_42(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_17(x)*F_4(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_75(x))
Eq(F_69(x), F_42(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_18(x) + F_43(x) + F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_2(x) + F_72(x))
Eq(F_75(x), F_65(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_17(x) + F_78(x))
Eq(F_81(x), F_2(x)*F_4(x))
Eq(F_82(x), F_18(x) + F_67(x) + F_83(x) + F_91(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_53(x))
Eq(F_87(x), F_56(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), 2*F_18(x) + F_60(x) + F_83(x))
Eq(F_90(x), F_63(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_17(x) + F_65(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_74(x) + F_80(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:
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