0123_0132_0321_1023_1302

Counting sequence:
1, 1, 2, 6, 19, 53, 146, 407, 1139, 3184, 8894, 24845, 69411, 193920, 541765, 1513553, 4228486, 11813334, 33003503, 92203529, 257593586, 719652027, 2010527707, 5616911372, 15692244990, 43840206217, 122478567127, 342174471792, 955949860377, 2670684726321, 7461224906298, 20844795551398, 58235143295675, 162694419636077, 454527501483554, 1269836114029039, 3547604383077619, 9911119017476376, 27689186721932350, 77356659724307701, 216115152236032155, 603771662226090832, 1686786957487926397, 4712460716458619489, 13165436159903815006, 36780934571006502902, 102756728412600116599, 287076588923442264161, 802020161414690447906, 2240643661427873264563, 6259797769474061408635, 17488308734348837053908, 48857958939078971084798, 136496912763451878161617, 381338222032256998150127, 1065363579575844989754272, 2976359281893985921896561, 8315203133228393844108449, 23230597047696766749086770, 64900475736536028438490950, 181315690775425596344486691, 506550673909196090276513509, 1415175841321273089906626546, 3953647216385659643633148551, 11045501099736094732426241587, 30858366431541132109045738624, 86210554887909612641629749182, 240850720033078991011719759005, 672876649684897654501461732947, 1879849002024942962867281537504, 5251827763779642610912260407541, 14672292737712510770632005689265, 40990714826146741714699150422518, 114517801136814323301731806031382, 319934083434078540954671790497983, 893815779963475966473835179629305, 2497097651917818270101720438747026, 6976266052797012455602398577029355, 19489941853907812539117551306014427, 54450021056236826534069407362860892, 152119735156119943281366282828217342, 424984478886946534068173835386458585, 1187300300710149467270638062984257351, 3317019971549153812564456093874347920, 9266923865070233808699083378184587017, 25889466647046286845056170248859050833, 72328692134284863528954981407036494826, 202068268812830595361733501545938652646, 564528184544064139930165682700964495691, 1577150499764073587181511158740791445149, 4406163885183155559851301022847341349378, 12309719450360956677290279942392240205663, 34390276189260736740240527162818160060979, 96077827049011587955172214543403469623464, 268417409609010001635306020591190074423614, 749891083032692881221243842153789021119493, 2095008059391796854486696666611159037064267, 5852928336161097578411793585709071233853744, 16351617338494926438909821211554812130355629, 45682327585090149884435132322585719671349825, 127624993319686714764437516145777598059068750

Generating function in Maple syntax:
(x-1)*(x^3+x^2+x-1)/(x^6+x^5-x^4-x^3+x^2-3*x+1)

Generating function in latex syntax:
\frac{\left(x -1\right) \left(x^{3}+x^{2}+x -1\right)}{x^{6}+x^{5}-x^{4}-x^{3}+x^{2}-3 x +1}

Generating function in sympy syntax:
(x - 1)*(x**3 + x**2 + x - 1)/(x**6 + x**5 - x**4 - x**3 + x**2 - 3*x + 1)

Implicit equation for the generating function in Maple syntax:
(x^6+x^5-x^4-x^3+x^2-3*x+1)*F(x)-(x-1)*(x^3+x^2+x-1) = 0

Implicit equation for the generating function in latex syntax:
\left(x^{6}+x^{5}-x^{4}-x^{3}+x^{2}-3 x +1\right) F \! \left(x \right)-\left(x -1\right) \left(x^{3}+x^{2}+x -1\right) = 0

Explicit closed form in Maple syntax:
-63638/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+4)-63638/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+4)-63638/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+4)-63638/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+4)-63638/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 5)^(-n+4)-63638/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 6)^(-n+4)-56031/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+3)-56031/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+3)-56031/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+3)-56031/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+3)-56031/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 5)^(-n+3)-56031/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 6)^(-n+3)-148717/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+2)-148717/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+2)-148717/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+2)-148717/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+2)-148717/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 5)^(-n+2)-148717/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 6)^(-n+2)+34574/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+1)+34574/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+1)+34574/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+1)+34574/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+1)+34574/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 5)^(-n+1)+34574/449573*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 6)^(-n+1)+104947/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n-1)+104947/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n-1)+104947/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^(-n-1)+104947/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)^(-n-1)+104947/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 5)^(-n-1)+104947/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 6)^(-n-1)+368042/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 1)^(-n)+368042/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 2)^(-n)+368042/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 3)^(-n)+368042/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 4)^(-n)+368042/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 5)^(-n)+368042/2247865*RootOf(_Z^6+_Z^5-_Z^4-_Z^3+_Z^2-3*_Z+1,index = 6)^(-n)

Explicit closed form in latex syntax:
-\frac{63638 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{2247865}-\frac{63638 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{2247865}-\frac{63638 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{2247865}-\frac{63638 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{2247865}-\frac{63638 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{2247865}-\frac{63638 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{2247865}-\frac{56031 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{449573}-\frac{56031 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{449573}-\frac{56031 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{449573}-\frac{56031 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{449573}-\frac{56031 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{449573}-\frac{56031 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{449573}-\frac{148717 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{2247865}-\frac{148717 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{2247865}-\frac{148717 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{2247865}-\frac{148717 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{2247865}-\frac{148717 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{2247865}-\frac{148717 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{2247865}+\frac{34574 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{449573}+\frac{34574 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{449573}+\frac{34574 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{449573}+\frac{34574 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{449573}+\frac{34574 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{449573}+\frac{34574 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{449573}+\frac{104947 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{2247865}+\frac{104947 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{2247865}+\frac{104947 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{2247865}+\frac{104947 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{2247865}+\frac{104947 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{2247865}+\frac{104947 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{2247865}+\frac{368042 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{2247865}+\frac{368042 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{2247865}+\frac{368042 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{2247865}+\frac{368042 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{2247865}+\frac{368042 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{2247865}+\frac{368042 \mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{2247865}

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 53
a(n+6) = -a(n)-a(n+1)+a(n+2)+a(n+3)-a(n+4)+3*a(n+5), n >= 6

Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 53
a \! \left(n +6\right) = -a \! \left(n \right)-a \! \left(n +1\right)+a \! \left(n +2\right)+a \! \left(n +3\right)-a \! \left(n +4\right)+3 a \! \left(n +5\right), \quad n \geq 6

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16213/
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[19,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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[14,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]+F[18,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[4,x]
F[18,x] = F[12,x]*F[4,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[15,x]+F[21,x]+F[74,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[32,x]
F[23,x] = F[24,x]+F[26,x]
F[24,x] = F[25,x]
F[25,x] = F[10,x]*F[4,x]
F[26,x] = F[15,x]+F[27,x]+F[30,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[17,x]+F[29,x]
F[29,x] = F[14,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[12,x]
F[32,x] = F[33,x]+F[38,x]
F[33,x] = F[15,x]+F[21,x]+F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[2,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[2,x]*F[4,x]
F[38,x] = F[15,x]+F[39,x]+F[48,x]+F[72,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[4,x]
F[44,x] = F[45,x]
F[45,x] = 2*F[15,x]+F[39,x]+F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[36,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[68,x]
F[50,x] = F[51,x]
F[51,x] = F[15,x]+F[37,x]+F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[56,x]
F[54,x] = F[4,x]+F[55,x]
F[55,x] = F[15,x]+F[18,x]+F[27,x]
F[56,x] = F[51,x]+F[57,x]
F[57,x] = F[15,x]+F[48,x]+F[58,x]+F[65,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[62,x]
F[60,x] = F[61,x]
F[61,x] = x^2
F[62,x] = F[63,x]
F[63,x] = 2*F[15,x]+F[58,x]+F[64,x]
F[64,x] = F[36,x]*F[4,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[35,x]*F[4,x]
F[68,x] = F[69,x]
F[69,x] = 2*F[15,x]+F[65,x]+F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[51,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[66,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[2,x]+F[51,x]
F[77,x] = F[66,x]+F[69,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_{19}\! \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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)+F_{21}\! \left(x \right)+F_{74}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{32}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right)+F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{17}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{14}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)
F_{33}\! \left(x \right) = F_{15}\! \left(x \right)+F_{21}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right)+F_{39}\! \left(x \right)+F_{48}\! \left(x \right)+F_{72}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \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_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{39}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{36}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{68}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right)+F_{37}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{56}\! \left(x \right) = F_{51}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)+F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = x^{2}
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \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) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{65}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{51}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{66}\! \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_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{2}\! \left(x \right)+F_{51}\! \left(x \right)
F_{77}\! \left(x \right) = F_{66}\! \left(x \right)+F_{69}\! \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_19(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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_14(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_18(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_4(x))
Eq(F_18(x), F_12(x)*F_4(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_15(x) + F_21(x) + F_74(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_32(x))
Eq(F_23(x), F_24(x) + F_26(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_10(x)*F_4(x))
Eq(F_26(x), F_15(x) + F_27(x) + F_30(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_17(x) + F_29(x))
Eq(F_29(x), F_14(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_12(x))
Eq(F_32(x), F_33(x) + F_38(x))
Eq(F_33(x), F_15(x) + F_21(x) + F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_2(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_2(x)*F_4(x))
Eq(F_38(x), F_15(x) + F_39(x) + F_48(x) + F_72(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_4(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), 2*F_15(x) + F_39(x) + F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_36(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_68(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_15(x) + F_37(x) + F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_56(x))
Eq(F_54(x), F_4(x) + F_55(x))
Eq(F_55(x), F_15(x) + F_18(x) + F_27(x))
Eq(F_56(x), F_51(x) + F_57(x))
Eq(F_57(x), F_15(x) + F_48(x) + F_58(x) + F_65(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_62(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), x**2)
Eq(F_62(x), F_63(x))
Eq(F_63(x), 2*F_15(x) + F_58(x) + F_64(x))
Eq(F_64(x), F_36(x)*F_4(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_35(x)*F_4(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), 2*F_15(x) + F_65(x) + F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_51(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_66(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_2(x) + F_51(x))
Eq(F_77(x), F_66(x) + F_69(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, 1, 3, 2], "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, 2, 3], "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, 1, 3, 2], "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, 2, 3], "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, 1, 3, 2], "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, 2, 3], "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, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "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": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [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]]}], "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, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "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, 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