0132_1203_2103
Counting sequence:
1, 1, 2, 6, 21, 75, 267, 950, 3384, 12065, 43034, 153524, 547744, 1954328, 6973114, 24880601, 88776363, 316763410, 1130246720, 4032847433, 14389658085, 51343944371, 183201075822, 653682454214, 2332414030833, 8322321077596, 29694997352494, 105955161038956, 378060184065944, 1348962159690978, 4813251925328713, 17174235714353261, 61279645647221382, 218652814206748270, 780178355414713393, 2783765982942551307, 9932796768894693879, 35441359746809468898, 126458842351207917740, 451219674500683735549, 1610003625457175886506, 5744677859745448083348, 20497670434053140395032, 73138042459649557233692, 260964936090636003982066, 931152866257840705447289, 3322460378504878838636503, 11854920246444396440022766, 42299717088816157777025944, 150930249094719535749663229, 538536464533872740089197261, 1921559961453677475483658231, 6856346651768118972981266978, 24464232369646583247747342634, 87291191042932824394000479917, 311464995858518031275952129820, 1111342879918244740981463425942, 3965399043769305671851514314404, 14148999251683043953280211796188, 50485254476137912674797492632978, 180137186678925320134258945982065, 642750172526818708152128294229145, 2293406441500665566990887556922922, 8183137602654295008420539636523430, 29198374876874282601240744775075021, 104183155269679254650041381775601291, 371737464421103511362952653528551763, 1326401970611545639675085287654149342, 4732754580929760715069951354742309856, 16887011946298946195833577137779523241, 60254798257132694711314423063996235834, 214996041013843964245225438492239582532, 767130568662301808622306334647630443200, 2737209981174735736642322161145588489808, 9766679607237483460145682389794428183674, 34848634633975208473317178962056596837433, 124343931068687793113035554345475611193699, 443673428127387355509127626240114251216426, 1583077751640084760830850426406417951365056, 5648603249276098766985686888802686655157137, 20154865188823993978038219645607036062180693, 71914873970256012647017573491407325327121643, 256600530428036545175820828509980606665343558, 915580165560503015707954647485042880376591246, 3266895193745108711746569247621880806179539417, 11656657285035548826631955579939351741310920188, 41592292070136684375689993412332536181287739630, 148406075373629658530845296265226060825138341740, 529529922771843742849585052120105881038327715664, 1889423585960413744840875361550098007143710654546, 6741680372842056648827938136013327000423390739705, 24055089915933791500275955164914285275469738129349, 85831323774212407494731141384982825803264746936110, 306256021764186399464926111979270639059864343367150, 1092756662049821222694797095714353675703463890748841, 3899081283612191587492901206253415507362993907372747, 13912369866221656887839335698888326656639381506647711, 49640933649692945166116061497388302605663805076535850, 177124552991952238833072720930999272928700521038852884, 632000749502280074188979487900300829291398989093624613, 2255051265476401125745890689879865432833068368049250378
Generating function in Maple syntax:
-(2*x^5-8*x^4+12*x^3-12*x^2+6*x-1)/(x^2-x+1)/(x^4-5*x^3+10*x^2-6*x+1)
Generating function in latex syntax:
-\frac{2 x^{5}-8 x^{4}+12 x^{3}-12 x^{2}+6 x -1}{\left(x^{2}-x +1\right) \left(x^{4}-5 x^{3}+10 x^{2}-6 x +1\right)}
Generating function in sympy syntax:
(-2*x**5 + 8*x**4 - 12*x**3 + 12*x**2 - 6*x + 1)/((x**2 - x + 1)*(x**4 - 5*x**3 + 10*x**2 - 6*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-x+1)*(x^4-5*x^3+10*x^2-6*x+1)*F(x)+2*x^5-8*x^4+12*x^3-12*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-x +1\right) \left(x^{4}-5 x^{3}+10 x^{2}-6 x +1\right) F \! \left(x \right)+2 x^{5}-8 x^{4}+12 x^{3}-12 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
-2510/167817*Sum(_alpha^(-n+4),_alpha = RootOf(_Z^6-6*_Z^5+16*_Z^4-21*_Z^3+17*_Z^2-7*_Z+1))+11111/167817*Sum(_alpha^(-n+3),_alpha = RootOf(_Z^6-6*_Z^5+16*_Z^4-21*_Z^3+17*_Z^2-7*_Z+1))-44542/167817*Sum(_alpha^(-n+2),_alpha = RootOf(_Z^6-6*_Z^5+16*_Z^4-21*_Z^3+17*_Z^2-7*_Z+1))+88537/167817*Sum(_alpha^(-n+1),_alpha = RootOf(_Z^6-6*_Z^5+16*_Z^4-21*_Z^3+17*_Z^2-7*_Z+1))-58421/167817*Sum(_alpha^(-n),_alpha = RootOf(_Z^6-6*_Z^5+16*_Z^4-21*_Z^3+17*_Z^2-7*_Z+1))+16384/167817*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^6-6*_Z^5+16*_Z^4-21*_Z^3+17*_Z^2-7*_Z+1))
Explicit closed form in latex syntax:
-\frac{2510 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-6 \textit{\_Z}^{5}+16 \textit{\_Z}^{4}-21 \textit{\_Z}^{3}+17 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +4}\right)}{167817}+\frac{11111 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-6 \textit{\_Z}^{5}+16 \textit{\_Z}^{4}-21 \textit{\_Z}^{3}+17 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +3}\right)}{167817}-\frac{44542 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-6 \textit{\_Z}^{5}+16 \textit{\_Z}^{4}-21 \textit{\_Z}^{3}+17 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{167817}+\frac{88537 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-6 \textit{\_Z}^{5}+16 \textit{\_Z}^{4}-21 \textit{\_Z}^{3}+17 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{167817}-\frac{58421 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-6 \textit{\_Z}^{5}+16 \textit{\_Z}^{4}-21 \textit{\_Z}^{3}+17 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{167817}+\frac{16384 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-6 \textit{\_Z}^{5}+16 \textit{\_Z}^{4}-21 \textit{\_Z}^{3}+17 \textit{\_Z}^{2}-7 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{167817}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 75
a(n+6) = -a(n)+6*a(n+1)-16*a(n+2)+21*a(n+3)-17*a(n+4)+7*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) = 21
a \! \left(5\right) = 75
a \! \left(n +6\right) = -a \! \left(n \right)+6 a \! \left(n +1\right)-16 a \! \left(n +2\right)+21 a \! \left(n +3\right)-17 a \! \left(n +4\right)+7 a \! \left(n +5\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14716/
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[29,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[16,x]+F[23,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[11,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[4,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[22,x]+F[7,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[22,x]+F[28,x]
F[28,x] = F[26,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[15,x]+F[31,x]+F[96,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[49,x]
F[33,x] = F[34,x]+F[7,x]
F[34,x] = F[15,x]+F[16,x]+F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[24,x]+F[37,x]
F[37,x] = F[34,x]+F[38,x]
F[38,x] = 2*F[15,x]+F[39,x]+F[43,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[27,x]+F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[34,x]+F[42,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[42,x]+F[48,x]
F[48,x] = F[46,x]
F[49,x] = F[50,x]+F[71,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[56,x]
F[53,x] = F[2,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[53,x]
F[56,x] = F[50,x]+F[57,x]
F[57,x] = 2*F[15,x]+F[58,x]+F[65,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[63,x]
F[60,x] = F[54,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[60,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[50,x]+F[64,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[64,x]+F[70,x]
F[70,x] = F[68,x]
F[71,x] = 2*F[15,x]+F[72,x]+F[82,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[60,x]+F[74,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[30,x]+F[75,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[75,x]+F[81,x]
F[81,x] = F[79,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[77,x]+F[84,x]
F[84,x] = F[71,x]+F[85,x]
F[85,x] = 3*F[15,x]+F[86,x]+F[90,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[80,x]+F[88,x]
F[88,x] = F[89,x]+F[92,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[71,x]+F[89,x]
F[92,x] = F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[89,x]+F[95,x]
F[95,x] = F[93,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[53,x]+F[98,x]
F[98,x] = F[30,x]+F[99,x]
F[99,x] = 2*F[15,x]+F[72,x]+F[76,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_{29}\! \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_{16}\! \left(x \right)+F_{23}\! \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_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \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_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{22}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)+F_{96}\! \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_{49}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{24}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{27}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \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_{42}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{71}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \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_{56}\! \left(x \right)
F_{53}\! \left(x \right) = F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{15}\! \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_{63}\! \left(x \right)
F_{60}\! \left(x \right) = F_{54}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \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_{50}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{64}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{72}\! \left(x \right)+F_{82}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{60}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{78}\! \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_{30}\! \left(x \right)+F_{75}\! \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_{75}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{77}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{71}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{86}\! \left(x \right)+F_{90}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{80}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{92}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{71}\! \left(x \right)+F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{89}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{53}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{30}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{72}\! \left(x \right)+F_{76}\! \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_29(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) + F_16(x) + F_23(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_11(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_4(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_22(x) + F_7(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_22(x) + F_28(x))
Eq(F_28(x), F_26(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_15(x) + F_31(x) + F_96(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_49(x))
Eq(F_33(x), F_34(x) + F_7(x))
Eq(F_34(x), F_15(x) + F_16(x) + F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_24(x) + F_37(x))
Eq(F_37(x), F_34(x) + F_38(x))
Eq(F_38(x), 2*F_15(x) + F_39(x) + F_43(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_27(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_34(x) + F_42(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_42(x) + F_48(x))
Eq(F_48(x), F_46(x))
Eq(F_49(x), F_50(x) + F_71(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_56(x))
Eq(F_53(x), F_2(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_53(x))
Eq(F_56(x), F_50(x) + F_57(x))
Eq(F_57(x), 2*F_15(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_63(x))
Eq(F_60(x), F_54(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_60(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_50(x) + F_64(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_64(x) + F_70(x))
Eq(F_70(x), F_68(x))
Eq(F_71(x), 2*F_15(x) + F_72(x) + F_82(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_60(x) + F_74(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_30(x) + F_75(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_75(x) + F_81(x))
Eq(F_81(x), F_79(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_77(x) + F_84(x))
Eq(F_84(x), F_71(x) + F_85(x))
Eq(F_85(x), 3*F_15(x) + F_86(x) + F_90(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_80(x) + F_88(x))
Eq(F_88(x), F_89(x) + F_92(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_71(x) + F_89(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_89(x) + F_95(x))
Eq(F_95(x), F_93(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_53(x) + F_98(x))
Eq(F_98(x), F_30(x) + F_99(x))
Eq(F_99(x), 2*F_15(x) + F_72(x) + F_76(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": 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