0123_0321_1230_2031
Counting sequence:
1, 1, 2, 6, 20, 59, 159, 421, 1102, 2851, 7300, 18532, 46711, 117027, 291669, 723646, 1788275, 4403660, 10810136, 26462275, 64613287, 157404905, 382653554, 928457711, 2248824828, 5438090304, 13130697807, 31661192683, 76244277873, 183385870218, 440592864839, 1057433540516, 2535367477436, 6073326162283, 14535619888863, 34760274091581, 83060618789094, 198329602734491, 473235147713924, 1128441126259836, 2689103564147399, 6404364985221347, 15243925660059229, 36264458776064294, 86226322584566075, 204919253937506124, 486764852666723584, 1155734080891059571, 2742881639402573767, 6506903014352937121, 15430036072857220330, 36575619550009964647, 86667245630728820316, 205287686987434330392, 486094972114707794719, 1150628386458780255371, 2722763284905455261465, 6440956788173059387730, 15232149216862292056591, 36011951380483948254340, 85115949222782584830692, 201121273297908717383195, 475107190917217838784479, 1122058008023886520650261, 2649308556467456915721918, 6253837019866825686097299, 14759120232255099398159812, 34823887335938356721052948, 82148518550953166842199703, 193745065209269439535011683, 456848909996811314203284389, 1077030642523479511751362766, 2538630181714068798419698051, 5982587012209717451894082828, 14096101348622134945692504168, 33207143626546626677172219171, 78214734241084468844153106599, 184192577144346176664361449881, 433694632884535190044820973474, 1021000955922705963009524226911, 2403256718804844464096998311164, 5655978768111711408141494254192, 13309157892616122235086409614959, 31313393828679042555456688916459, 73662755124386470011621020885505, 173262859708296535951962430484314, 407477934661742480154699838780759, 958175718019572845693018983826596, 2252838059609171683345020162785932, 5296144138250879306198075019682891, 12449039443951438665654684088696735, 29258987399718549507920058641678637, 68759273903779736749949683441241046, 161567094579565739041609227017866507, 379599174378197508496090737383544644, 891762791028116138212140116164695596, 2094720974483174957272719005317831655, 4919905167248048072899549250080192675, 11554254770233148062277489908449861421, 27132056782590775740610217834975663030, 63705943268888920126272907375225398347
Generating function in Maple syntax:
(2*x^9-5*x^8+7*x^7-2*x^6-5*x^5+6*x^4-7*x^3+9*x^2-5*x+1)/(x^3-2*x^2+3*x-1)^2
Generating function in latex syntax:
\frac{2 x^{9}-5 x^{8}+7 x^{7}-2 x^{6}-5 x^{5}+6 x^{4}-7 x^{3}+9 x^{2}-5 x +1}{\left(x^{3}-2 x^{2}+3 x -1\right)^{2}}
Generating function in sympy syntax:
(2*x**9 - 5*x**8 + 7*x**7 - 2*x**6 - 5*x**5 + 6*x**4 - 7*x**3 + 9*x**2 - 5*x + 1)/(x**3 - 2*x**2 + 3*x - 1)**2
Implicit equation for the generating function in Maple syntax:
-(x^3-2*x^2+3*x-1)^2*F(x)+2*x^9-5*x^8+7*x^7-2*x^6-5*x^5+6*x^4-7*x^3+9*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{3}-2 x^{2}+3 x -1\right)^{2} F \! \left(x \right)+2 x^{9}-5 x^{8}+7 x^{7}-2 x^{6}-5 x^{5}+6 x^{4}-7 x^{3}+9 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
1/529*(-46*n-1375)*Sum(_alpha^(-1-n),_alpha = RootOf(_Z^3-2*_Z^2+3*_Z-1))-1275/529*Sum(_alpha^(1-n),_alpha = RootOf(_Z^3-2*_Z^2+3*_Z-1))+1/529*(184*n+3812)*Sum(_alpha^(-n),_alpha = RootOf(_Z^3-2*_Z^2+3*_Z-1))+piecewise(n = 0,-8,n = 1,-1,n = 2,3,n = 3,2,0)
Explicit closed form in latex syntax:
\frac{\left(-46 n -1375\right) \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{3}-2 \textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-1-n}\right)}{529}-\frac{1275 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{3}-2 \textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{1-n}\right)}{529}+\frac{\left(184 n +3812\right) \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{3}-2 \textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{529}+\left(\left\{\begin{array}{cc}-8 & n =0 \\ -1 & n =1 \\ 3 & n =2 \\ 2 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 59
a(6) = 159
a(7) = 421
a(8) = 1102
a(9) = 2851
a(n+6) = -a(n)+4*a(n+1)-10*a(n+2)+14*a(n+3)-13*a(n+4)+6*a(n+5), n >= 10
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(5\right) = 59
a \! \left(6\right) = 159
a \! \left(7\right) = 421
a \! \left(8\right) = 1102
a \! \left(9\right) = 2851
a \! \left(n +6\right) = -a \! \left(n \right)+4 a \! \left(n +1\right)-10 a \! \left(n +2\right)+14 a \! \left(n +3\right)-13 a \! \left(n +4\right)+6 a \! \left(n +5\right), \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15103/
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[26,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[21,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[15,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[4,x]
F[26,x] = F[2,x]+F[27,x]
F[27,x] = F[18,x]+F[28,x]+F[64,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[36,x]
F[30,x] = F[31,x]+F[7,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[11,x]
F[35,x] = F[19,x]
F[36,x] = F[27,x]+F[37,x]
F[37,x] = 2*F[18,x]+F[38,x]+F[42,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[31,x]
F[41,x] = F[37,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[56,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[50,x]
F[48,x] = F[11,x]+F[49,x]
F[49,x] = F[32,x]
F[50,x] = F[45,x]+F[51,x]
F[51,x] = 2*F[18,x]+F[42,x]+F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[49,x]
F[55,x] = F[51,x]
F[56,x] = F[57,x]
F[57,x] = 2*F[18,x]+F[58,x]+F[62,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[19,x]
F[61,x] = F[57,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[45,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[2,x]+F[45,x]
F[67,x] = F[107,x]+F[68,x]
F[68,x] = F[105,x]+F[18,x]+F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[77,x]
F[71,x] = F[15,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[4,x]
F[76,x] = F[23,x]
F[77,x] = F[68,x]+F[78,x]
F[78,x] = 2*F[18,x]+F[79,x]+F[83,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[72,x]
F[82,x] = F[78,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[97,x]
F[85,x] = F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[91,x]
F[89,x] = F[4,x]+F[90,x]
F[90,x] = F[73,x]
F[91,x] = F[86,x]+F[92,x]
F[92,x] = 2*F[18,x]+F[83,x]+F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[90,x]
F[96,x] = F[92,x]
F[97,x] = F[98,x]
F[98,x] = 2*F[18,x]+F[103,x]+F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[23,x]
F[102,x] = F[98,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[86,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[2,x]+F[86,x]
F[107,x] = 2*F[18,x]+F[58,x]+F[62,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_{26}\! \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_{21}\! \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_{11}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)+F_{64}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{36}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{7}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{38}\! \left(x \right)+F_{42}\! \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_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{31}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{56}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \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_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{32}\! \left(x \right)
F_{50}\! \left(x \right) = F_{45}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{42}\! \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_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \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_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{19}\! \left(x \right)
F_{61}\! \left(x \right) = F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{45}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{2}\! \left(x \right)+F_{45}\! \left(x \right)
F_{67}\! \left(x \right) = F_{107}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{105}\! \left(x \right)+F_{18}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \left(x \right)
F_{71}\! \left(x \right) = F_{15}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right)
F_{76}\! \left(x \right) = F_{23}\! \left(x \right)
F_{77}\! \left(x \right) = F_{68}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{79}\! \left(x \right)+F_{83}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{72}\! \left(x \right)
F_{82}\! \left(x \right) = F_{78}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{97}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{73}\! \left(x \right)
F_{91}\! \left(x \right) = F_{86}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{83}\! \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_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{90}\! \left(x \right)
F_{96}\! \left(x \right) = F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{103}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{23}\! \left(x \right)
F_{102}\! \left(x \right) = F_{98}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{86}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{2}\! \left(x \right)+F_{86}\! \left(x \right)
F_{107}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \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_26(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_21(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_15(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_4(x))
Eq(F_26(x), F_2(x) + F_27(x))
Eq(F_27(x), F_18(x) + F_28(x) + F_64(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_36(x))
Eq(F_30(x), F_31(x) + F_7(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_11(x))
Eq(F_35(x), F_19(x))
Eq(F_36(x), F_27(x) + F_37(x))
Eq(F_37(x), 2*F_18(x) + F_38(x) + F_42(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_31(x))
Eq(F_41(x), F_37(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_56(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_50(x))
Eq(F_48(x), F_11(x) + F_49(x))
Eq(F_49(x), F_32(x))
Eq(F_50(x), F_45(x) + F_51(x))
Eq(F_51(x), 2*F_18(x) + F_42(x) + F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_51(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), 2*F_18(x) + F_58(x) + F_62(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_19(x))
Eq(F_61(x), F_57(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_45(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_2(x) + F_45(x))
Eq(F_67(x), F_107(x) + F_68(x))
Eq(F_68(x), F_105(x) + F_18(x) + F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_77(x))
Eq(F_71(x), F_15(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_4(x))
Eq(F_76(x), F_23(x))
Eq(F_77(x), F_68(x) + F_78(x))
Eq(F_78(x), 2*F_18(x) + F_79(x) + F_83(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_72(x))
Eq(F_82(x), F_78(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_97(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_91(x))
Eq(F_89(x), F_4(x) + F_90(x))
Eq(F_90(x), F_73(x))
Eq(F_91(x), F_86(x) + F_92(x))
Eq(F_92(x), 2*F_18(x) + F_83(x) + F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_90(x))
Eq(F_96(x), F_92(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_103(x) + 2*F_18(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_23(x))
Eq(F_102(x), F_98(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_86(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_2(x) + F_86(x))
Eq(F_107(x), 2*F_18(x) + F_58(x) + F_62(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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "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, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"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": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "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": [2, 0, 3, 1], "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, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "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, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "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": [2, 0, 3, 1], "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": [2, 0, 3, 1], "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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], 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