0123_0213_0321_1302
Counting sequence:
1, 1, 2, 6, 20, 63, 191, 572, 1712, 5132, 15397, 46201, 138622, 415890, 1247696, 3743123, 11229439, 33688472, 101065732, 303197784, 909594393, 2728785009, 8186358298, 24559080846, 73677253452, 221031780343, 663095377471, 1989286198644, 5967858716200, 17903576367140, 53710729498909, 161132189220073, 483396568976598, 1450189709324922, 4350569132331848, 13051707404921131, 39155122229180415, 117465366713767760, 352396100189014428, 1057188300653839792, 3171564902119418993, 9514694706645503969, 28544084120459061682, 85632252362327789526, 256896757088712679300, 770690271269283953391, 2312070813813574828735, 6936212441451135560620, 20808637324372346225632, 62425911973151492969020, 187277735919517157195093, 561833207758665494191193, 1685499623276203909363118, 5056498869828989073220386, 15169496609487653675579584, 45508489828464209808496387, 136525469485394901174927359, 409576408456188836228873224, 1228729225368574026788254580, 3686187676105735757088590856, 11058563028317232151585878537, 33175689084951741716352198225, 99527067254855307487705426634, 298581201764566072251323021022, 895743605293698489244557459132, 2687230815881095963441060736807, 8061692447643288792100437673535, 24185077342929868016789709468900, 72555232028789607034700528117720, 217665696086368826533115237963860, 652997088259106489475658127502029, 1958991264777319486393690458664649, 5876973794331958491865627416960006, 17630921382995875535055728212523658, 52892764148987626713333082889372728, 158678292446962880336771677655717147, 476034877340888641368278027177152767, 1428104632022665924756030521412110784, 4284313896067997775452730228487686540, 12852941688203993328513252781772765024, 38558825064611979989460188075584002529, 115676475193835939975512502232752020417, 347029425581507819939511732286020036962, 1041088276744523459842137551429927412390, 3123264830233570379569349408978357934836, 9369794490700711138786157590878962981535, 28109383472102133416500567180562460659903, 84328150416306400249760195782892872593692, 252984451248919200749750832967150839351824, 758953353746757602250107956805122171818092, 2276860061240272806751880095920089874359173, 6830580183720818420258471330423108450689081, 20491740551162455260780564146265813633520606, 61475221653487365782351061459206782274754738, 184425664960462097347070228242026468288999344, 553276994881386292041241690455729072247689587, 1659830984644158876123781476138323684146584319, 4979492953932476628371447038424246915347153016, 14938478861797429885114527780581214721398539236, 44815436585392289655343922918142024636328865208, 134446309756176868966032386502476205729626013177
Generating function in Maple syntax:
-(x-1)*(2*x-1)^2/(3*x-1)/(x^4+x^3-3*x^2+3*x-1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(2 x -1\right)^{2}}{\left(3 x -1\right) \left(x^{4}+x^{3}-3 x^{2}+3 x -1\right)}
Generating function in sympy syntax:
(1 - x)*(2*x - 1)**2/((3*x - 1)*(x**4 + x**3 - 3*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(3*x-1)*(x^4+x^3-3*x^2+3*x-1)*F(x)+(x-1)*(2*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x -1\right) \left(x^{4}+x^{3}-3 x^{2}+3 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(2 x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-77064/149707*Sum(_alpha^(-n+3),_alpha = RootOf(3*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1))-101536/149707*Sum(_alpha^(-n+2),_alpha = RootOf(3*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1))+193449/149707*Sum(_alpha^(-n+1),_alpha = RootOf(3*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1))-146023/149707*Sum(_alpha^(-n),_alpha = RootOf(3*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1))+44910/149707*Sum(_alpha^(-n-1),_alpha = RootOf(3*_Z^5+2*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1))
Explicit closed form in latex syntax:
-\frac{77064 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +3}\right)}{149707}-\frac{101536 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{149707}+\frac{193449 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{149707}-\frac{146023 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{149707}+\frac{44910 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+2 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{149707}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n+5) = -3*a(n)-2*a(n+1)+10*a(n+2)-12*a(n+3)+6*a(n+4), n >= 5
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) = 20
a \! \left(n +5\right) = -3 a \! \left(n \right)-2 a \! \left(n +1\right)+10 a \! \left(n +2\right)-12 a \! \left(n +3\right)+6 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14909/
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[20,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[18,x] = F[19,x]*F[4,x]
F[19,x] = F[15,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[107,x]+F[22,x]+F[23,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[36,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[22,x]+F[27,x]+F[34,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[33,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[4,x]
F[33,x] = F[17,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[14,x]
F[36,x] = F[21,x]+F[37,x]
F[37,x] = F[104,x]+F[22,x]+F[38,x]+F[81,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[47,x]
F[40,x] = F[26,x]+F[41,x]
F[41,x] = F[22,x]+F[42,x]+F[44,x]+F[46,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[30,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[33,x]
F[46,x] = 0
F[47,x] = F[37,x]+F[48,x]
F[48,x] = F[22,x]+F[49,x]+F[53,x]+F[71,x]+F[80,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[41,x]
F[52,x] = F[48,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = 2*F[22,x]+F[56,x]+F[67,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[60,x]
F[58,x] = F[30,x]+F[59,x]
F[59,x] = F[42,x]
F[60,x] = F[55,x]+F[61,x]
F[61,x] = 2*F[22,x]+F[53,x]+F[62,x]+F[66,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[59,x]
F[65,x] = F[61,x]
F[66,x] = 0
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[2,x]*F[4,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[2,x]+F[69,x]
F[80,x] = 0
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[73,x]+F[83,x]
F[83,x] = F[55,x]+F[84,x]
F[84,x] = F[103,x]+F[22,x]+F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[89,x]
F[87,x] = F[11,x]+F[88,x]
F[88,x] = F[18,x]+F[22,x]+F[27,x]
F[89,x] = F[84,x]+F[90,x]
F[90,x] = F[22,x]+F[75,x]+F[81,x]+F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[96,x]
F[93,x] = F[88,x]+F[94,x]
F[94,x] = F[22,x]+F[42,x]+F[44,x]+F[95,x]
F[95,x] = 0
F[96,x] = F[90,x]+F[97,x]
F[97,x] = F[102,x]+F[22,x]+F[53,x]+F[71,x]+F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[94,x]
F[101,x] = F[97,x]
F[102,x] = 0
F[103,x] = F[4,x]*F[79,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]
F[106,x] = F[74,x]+F[77,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[106,x]+F[109,x]
F[109,x] = F[2,x]+F[84,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_{20}\! \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_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{107}\! \left(x \right)+F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{36}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{34}\! \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_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{17}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{14}\! \left(x \right)
F_{36}\! \left(x \right) = F_{21}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{104}\! \left(x \right)+F_{22}\! \left(x \right)+F_{38}\! \left(x \right)+F_{81}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{40}\! \left(x \right) = F_{26}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{30}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{33}\! \left(x \right)
F_{46}\! \left(x \right) = 0
F_{47}\! \left(x \right) = F_{37}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{22}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)+F_{71}\! \left(x \right)+F_{80}\! \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_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{41}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{56}\! \left(x \right)+F_{67}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{30}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{42}\! \left(x \right)
F_{60}\! \left(x \right) = F_{55}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{53}\! \left(x \right)+F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = 0
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_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \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_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{2}\! \left(x \right)+F_{69}\! \left(x \right)
F_{80}\! \left(x \right) = 0
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{73}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{55}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{103}\! \left(x \right)+F_{22}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{11}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{89}\! \left(x \right) = F_{84}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{22}\! \left(x \right)+F_{75}\! \left(x \right)+F_{81}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{96}\! \left(x \right)
F_{93}\! \left(x \right) = F_{88}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = 0
F_{96}\! \left(x \right) = F_{90}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{102}\! \left(x \right)+F_{22}\! \left(x \right)+F_{53}\! \left(x \right)+F_{71}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{94}\! \left(x \right)
F_{101}\! \left(x \right) = F_{97}\! \left(x \right)
F_{102}\! \left(x \right) = 0
F_{103}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{74}\! \left(x \right)+F_{77}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{2}\! \left(x \right)+F_{84}\! \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_20(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))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_15(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_107(x) + F_22(x) + F_23(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_36(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_34(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_33(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_4(x))
Eq(F_33(x), F_17(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_14(x))
Eq(F_36(x), F_21(x) + F_37(x))
Eq(F_37(x), F_104(x) + F_22(x) + F_38(x) + F_81(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_47(x))
Eq(F_40(x), F_26(x) + F_41(x))
Eq(F_41(x), F_22(x) + F_42(x) + F_44(x) + F_46(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_30(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_33(x))
Eq(F_46(x), 0)
Eq(F_47(x), F_37(x) + F_48(x))
Eq(F_48(x), F_22(x) + F_49(x) + F_53(x) + F_71(x) + F_80(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_41(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), 2*F_22(x) + F_56(x) + F_67(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_60(x))
Eq(F_58(x), F_30(x) + F_59(x))
Eq(F_59(x), F_42(x))
Eq(F_60(x), F_55(x) + F_61(x))
Eq(F_61(x), 2*F_22(x) + F_53(x) + F_62(x) + F_66(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_59(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), 0)
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_2(x)*F_4(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_2(x) + F_69(x))
Eq(F_80(x), 0)
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_73(x) + F_83(x))
Eq(F_83(x), F_55(x) + F_84(x))
Eq(F_84(x), F_103(x) + F_22(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_89(x))
Eq(F_87(x), F_11(x) + F_88(x))
Eq(F_88(x), F_18(x) + F_22(x) + F_27(x))
Eq(F_89(x), F_84(x) + F_90(x))
Eq(F_90(x), F_22(x) + F_75(x) + F_81(x) + F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_96(x))
Eq(F_93(x), F_88(x) + F_94(x))
Eq(F_94(x), F_22(x) + F_42(x) + F_44(x) + F_95(x))
Eq(F_95(x), 0)
Eq(F_96(x), F_90(x) + F_97(x))
Eq(F_97(x), F_102(x) + F_22(x) + F_53(x) + F_71(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_94(x))
Eq(F_101(x), F_97(x))
Eq(F_102(x), 0)
Eq(F_103(x), F_4(x)*F_79(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_74(x) + F_77(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_106(x) + F_109(x))
Eq(F_109(x), F_2(x) + F_84(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, 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, 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, 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, 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, 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, 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": [1, 0, 2], "pos": [[0, 1], [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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [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": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"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]]}], "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": [1, 0, 2], "pos": [[1, 2], [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, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [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": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"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]]}], "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": [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": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [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": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"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]]}], "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": [1, 0, 2], "pos": [[0, 1], [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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [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": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"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]]}], "requirements": []}, "rule_class": "Rule", 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