0123_0321_1032_1302
Counting sequence:
1, 1, 2, 6, 20, 60, 176, 520, 1544, 4584, 13600, 40344, 119688, 355088, 1053464, 3125368, 9272192, 27508312, 81610408, 242118032, 718304696, 2131033496, 6322252672, 18756569976, 55646133640, 165088403280, 489776721496, 1453047168440, 4310833857664, 12789184654104, 37942367884520, 112565681051664, 333954712294008, 990761560907608, 2939346068301184, 8720317430687288, 25871038770163912, 76753014138222032, 227707330642479128, 675551690190917752, 2004195845747046016, 5945956536611622616, 17640191805754615592, 52334113952528151696, 155262454816547176760, 460625547181845855000, 1366562798245555922816, 4054255985092972570360, 12027981161030147851784, 35684064188852274540624, 105865848972203732756440, 314077957020005164572984, 931792112787576605747328, 2764398207664836667263128, 8201290122191351190700904, 24331212298524380445480208, 72184727414286616691760632, 214154346604047845345729752, 635343317239288382617790848, 1884907484539439296782124472, 5592057284415698431803563336, 16590259696394328454555606736, 49219223408324742290663087512, 146021340066490173874605031416, 433209430752765833105870346880, 1285225918401245466933443397720, 3812949451400600400024996084136, 11312083977439067747102495611280, 33560173179224625441361118238904, 99564786299838500310897738069144, 295384252577970211785587079359360, 876332485747399521422790727709304, 2599863123622354603987302816384648, 7713154962875281714732087356301648, 22883035241654230006625714866657624, 67888341980826916555965244331859128, 201408026873821792298708798474292352, 597528119049697483782876755536936472, 1772719084720232952175103386533550568, 5259221872820298790451781489676018192, 15602818825587701971343412190516961656, 46289729011482667995494415366015840856, 137330250123941365500393603659949698432, 407425102757157430029276782974219214136, 1208730153821671664521112400375773549000, 3586005316978705630525836456205032511440, 10638796502876642818115737741507661810456, 31562694704808881012922155135017938446200, 93638758553150754810744625376707765649024, 277803184594354080316594869390530747144664, 824173777645282533801115768547935676298280, 2445121054857412792734085997276727689940624, 7254073273221965514655821212816724419110968, 21521052689287756979468798917050378414278168, 63847674459646696076820979069983737556201344, 189420359345811087865773952713087738472429048, 561963655502806012508750119329013683527864072, 1667208061460475855773055961248021544052122192, 4946196596489537122695607627981193900685763288, 14674149757705369713062815066779763002005753912, 43534596110553135753056449733512165560491470976
Generating function in Maple syntax:
(x^3+2*x-1)/(2*x^4+2*x^3-x^2+3*x-1)
Generating function in latex syntax:
\frac{x^{3}+2 x -1}{2 x^{4}+2 x^{3}-x^{2}+3 x -1}
Generating function in sympy syntax:
(x**3 + 2*x - 1)/(2*x**4 + 2*x**3 - x**2 + 3*x - 1)
Implicit equation for the generating function in Maple syntax:
(2*x^4+2*x^3-x^2+3*x-1)*F(x)-x^3-2*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{4}+2 x^{3}-x^{2}+3 x -1\right) F \! \left(x \right)-x^{3}-2 x +1 = 0
Explicit closed form in Maple syntax:
91/1655*Sum(_alpha^(-n+2),_alpha = RootOf(2*_Z^4+2*_Z^3-_Z^2+3*_Z-1))+309/3310*Sum(_alpha^(-n+1),_alpha = RootOf(2*_Z^4+2*_Z^3-_Z^2+3*_Z-1))+843/3310*Sum(_alpha^(-n),_alpha = RootOf(2*_Z^4+2*_Z^3-_Z^2+3*_Z-1))-39/3310*Sum(_alpha^(-n-1),_alpha = RootOf(2*_Z^4+2*_Z^3-_Z^2+3*_Z-1))
Explicit closed form in latex syntax:
\frac{91 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{1655}+\frac{309 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{3310}+\frac{843 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{3310}-\frac{39 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{3310}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+4) = 2*a(n)+2*a(n+1)-a(n+2)+3*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) = 2 a \! \left(n \right)+2 a \! \left(n +1\right)-a \! \left(n +2\right)+3 a \! \left(n +3\right), \quad n \geq 4
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15093/
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[25,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[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[4,x]
F[21,x] = F[22,x]
F[22,x] = x^2
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[15,x]
F[25,x] = F[2,x]+F[26,x]
F[26,x] = F[18,x]+F[27,x]+F[94,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[40,x]
F[29,x] = F[15,x]+F[30,x]
F[30,x] = F[18,x]+F[31,x]+F[38,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[35,x]
F[33,x] = F[34,x]+F[4,x]
F[34,x] = F[22,x]
F[35,x] = F[36,x]
F[36,x] = F[18,x]+F[19,x]+F[37,x]
F[37,x] = F[15,x]*F[4,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[15,x]+F[36,x]
F[40,x] = F[41,x]+F[83,x]
F[41,x] = F[18,x]+F[27,x]+F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[2,x]+F[44,x]
F[44,x] = F[18,x]+F[45,x]+F[73,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[49,x]
F[47,x] = F[4,x]+F[48,x]
F[48,x] = F[18,x]+F[31,x]+F[37,x]
F[49,x] = F[44,x]+F[50,x]
F[50,x] = F[18,x]+F[51,x]+F[74,x]+F[78,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[60,x]
F[53,x] = F[54,x]+F[57,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[4,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[36,x]
F[60,x] = F[61,x]+F[64,x]
F[61,x] = 2*F[18,x]+F[51,x]+F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[44,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = 2*F[18,x]+F[68,x]+F[74,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[44,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[2,x]*F[4,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[2,x]+F[72,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[82,x]
F[80,x] = F[44,x]+F[81,x]
F[81,x] = F[71,x]
F[82,x] = F[67,x]
F[83,x] = F[18,x]+F[78,x]+F[84,x]+F[92,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = F[55,x]
F[88,x] = F[58,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = 2*F[18,x]+F[62,x]+F[84,x]
F[91,x] = F[65,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[67,x]+F[75,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[96,x]+F[99,x]
F[96,x] = F[2,x]+F[97,x]
F[97,x] = F[18,x]+F[45,x]+F[98,x]
F[98,x] = F[4,x]*F[77,x]
F[99,x] = F[100,x]+F[75,x]
F[100,x] = 2*F[18,x]+F[101,x]+F[68,x]
F[101,x] = F[102,x]*F[4,x]
F[102,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{25}\! \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_{14}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \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_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x^{2}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)+F_{94}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{40}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{18}\! \left(x \right)+F_{31}\! \left(x \right)+F_{38}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{22}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{83}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{18}\! \left(x \right)+F_{45}\! \left(x \right)+F_{73}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right)+F_{31}\! \left(x \right)+F_{37}\! \left(x \right)
F_{49}\! \left(x \right) = F_{44}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{18}\! \left(x \right)+F_{51}\! \left(x \right)+F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{60}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{36}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{51}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{44}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{68}\! \left(x \right)+F_{74}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{44}\! \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_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{2}\! \left(x \right)+F_{72}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{44}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{71}\! \left(x \right)
F_{82}\! \left(x \right) = F_{67}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right)+F_{78}\! \left(x \right)+F_{84}\! \left(x \right)+F_{92}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \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_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{55}\! \left(x \right)
F_{88}\! \left(x \right) = F_{58}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{62}\! \left(x \right)+F_{84}\! \left(x \right)
F_{91}\! \left(x \right) = F_{65}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{67}\! \left(x \right)+F_{75}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{99}\! \left(x \right)
F_{96}\! \left(x \right) = F_{2}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right)+F_{45}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{75}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{101}\! \left(x \right)+F_{68}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_25(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_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_4(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), x**2)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_15(x))
Eq(F_25(x), F_2(x) + F_26(x))
Eq(F_26(x), F_18(x) + F_27(x) + F_94(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_40(x))
Eq(F_29(x), F_15(x) + F_30(x))
Eq(F_30(x), F_18(x) + F_31(x) + F_38(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_35(x))
Eq(F_33(x), F_34(x) + F_4(x))
Eq(F_34(x), F_22(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_18(x) + F_19(x) + F_37(x))
Eq(F_37(x), F_15(x)*F_4(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_15(x) + F_36(x))
Eq(F_40(x), F_41(x) + F_83(x))
Eq(F_41(x), F_18(x) + F_27(x) + F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_2(x) + F_44(x))
Eq(F_44(x), F_18(x) + F_45(x) + F_73(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_49(x))
Eq(F_47(x), F_4(x) + F_48(x))
Eq(F_48(x), F_18(x) + F_31(x) + F_37(x))
Eq(F_49(x), F_44(x) + F_50(x))
Eq(F_50(x), F_18(x) + F_51(x) + F_74(x) + F_78(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_60(x))
Eq(F_53(x), F_54(x) + F_57(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_4(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_36(x))
Eq(F_60(x), F_61(x) + F_64(x))
Eq(F_61(x), 2*F_18(x) + F_51(x) + F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_44(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), 2*F_18(x) + F_68(x) + F_74(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_44(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_73(x))
Eq(F_73(x), F_2(x)*F_4(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_2(x) + F_72(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_82(x))
Eq(F_80(x), F_44(x) + F_81(x))
Eq(F_81(x), F_71(x))
Eq(F_82(x), F_67(x))
Eq(F_83(x), F_18(x) + F_78(x) + F_84(x) + F_92(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), F_55(x))
Eq(F_88(x), F_58(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), 2*F_18(x) + F_62(x) + F_84(x))
Eq(F_91(x), F_65(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_67(x) + F_75(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_99(x))
Eq(F_96(x), F_2(x) + F_97(x))
Eq(F_97(x), F_18(x) + F_45(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_77(x))
Eq(F_99(x), F_100(x) + F_75(x))
Eq(F_100(x), F_101(x) + 2*F_18(x) + F_68(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(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, 2, 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, 0, 3, 2], "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, 2, 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, 0, 3, 2], "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, 2, 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, 0, 3, 2], "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], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 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, 0, 3, 2], "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]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], 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