0132_0231_0321_1023_3102
Counting sequence:
1, 1, 2, 6, 19, 51, 129, 320, 782, 1890, 4531, 10791, 25557, 60240, 141402, 330702, 770915, 1791899, 4154169, 9607856, 22173478, 51072522, 117424291, 269530703, 617722605, 1413718240, 3231173298, 7376070102, 16818708979, 38308498435, 87168882225, 198160954464, 450079276606, 1021400989170, 2316114521299, 5248060365431, 11883099366213, 26888620134576, 60803666442506, 137412741513246, 310365028565955, 700613940192107, 1580723364394857, 3564628167755344, 8034583313119830, 18101398807965978, 40763259828749891, 91757484098161823, 206460638076705501, 464368912172055232, 1044060441949603170, 2346556060062989478, 5272114484662083795, 11841121449509200851, 26586437573639328993, 59674900313420667008, 133903575477545815406, 300376533945679458690, 673623769720156507379, 1510255371349807956679, 3385078734926142123957, 7585359957649511182096, 16993236979234920300986, 38060267536849009438062, 85224903436330653909283, 190793322354448565801787, 427036184094303843118233, 955594823727036868150000, 2137928352515271695792518, 4782172926386903724161322, 10694798303127055823392995, 23913185594728555750109935, 53459145425024416528902093, 119489149398162902997159328, 267029265516987562383884306, 596643840020046343880103030, 1332905216805336210040192179, 2977234254987754421669377955, 6649027625276790868212509841, 14846919405288469927735340448, 33147385497283892678885425310, 73994338758564208710467744274, 165152636137785704298909725203, 368563048635312133578928034583, 822391757892821772957254514981, 1834795834866064661341519054448, 4092984475115169110820389900906, 9129291543482248600803812533182, 20360100275491374486488800852867, 45401457490167270985435728828171, 101229682287314584981156522848969, 225681137730776945891304008601744, 503075351177103318554685807355062, 1121301096855783328073293512865338, 2498986428751524215445923946995843, 5568766021523895132049241587996991, 12408189477805322463359957837466045, 27644781157474847497950234831804800, 61584877695542690222121209558010562, 137180399924930651967133554714901830, 305539906892528727907064094994314643
Generating function in Maple syntax:
(x^2+x+1)*(x^6+2*x^5-2*x^4+6*x^3-9*x^2+5*x-1)/(x-1)/(x^3+2*x-1)^2
Generating function in latex syntax:
\frac{\left(x^{2}+x +1\right) \left(x^{6}+2 x^{5}-2 x^{4}+6 x^{3}-9 x^{2}+5 x -1\right)}{\left(x -1\right) \left(x^{3}+2 x -1\right)^{2}}
Generating function in sympy syntax:
(x**2 + x + 1)*(x**6 + 2*x**5 - 2*x**4 + 6*x**3 - 9*x**2 + 5*x - 1)/((x - 1)*(x**3 + 2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(x-1)*(x^3+2*x-1)^2*F(x)+(x^2+x+1)*(x^6+2*x^5-2*x^4+6*x^3-9*x^2+5*x-1) = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(x^{3}+2 x -1\right)^{2} F \! \left(x \right)+\left(x^{2}+x +1\right) \left(x^{6}+2 x^{5}-2 x^{4}+6 x^{3}-9 x^{2}+5 x -1\right) = 0
Explicit closed form in Maple syntax:
1/6962*(472*n+472)*Sum(_alpha^(-n-2),_alpha = RootOf(_Z^3+2*_Z-1))+1/6962*(-944*n+2263)*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^3+2*_Z-1))+1535/6962*Sum(_alpha^(1-n),_alpha = RootOf(_Z^3+2*_Z-1))+1/6962*(708*n-5619)*Sum(_alpha^(-n),_alpha = RootOf(_Z^3+2*_Z-1))+piecewise(n = 0,4,n = 1,1,0)-3/2
Explicit closed form in latex syntax:
\frac{\left(472 n +472\right) \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{3}+2 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -2}\right)}{6962}+\frac{\left(-944 n +2263\right) \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{3}+2 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{6962}+\frac{1535 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{3}+2 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{1-n}\right)}{6962}+\frac{\left(708 n -5619\right) \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{3}+2 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{6962}+\left(\left\{\begin{array}{cc}4 & n =0 \\ 1 & n =1 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)-\frac{3}{2}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(6) = 129
a(7) = 320
a(8) = 782
a(n) = -4*a(n+2)+2*a(n+3)-4*a(n+4)+4*a(n+5)-a(n+6)-6, n >= 9
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) = 51
a \! \left(6\right) = 129
a \! \left(7\right) = 320
a \! \left(8\right) = 782
a \! \left(n \right) = -4 a \! \left(n +2\right)+2 a \! \left(n +3\right)-4 a \! \left(n +4\right)+4 a \! \left(n +5\right)-a \! \left(n +6\right)-6, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18647/
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[18,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[11,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[4,x]
F[17,x] = F[15,x]
F[18,x] = F[19,x]+F[35,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[27,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[10,x]+F[26,x]
F[26,x] = F[11,x]
F[27,x] = F[19,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[19,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]*F[4,x]
F[34,x] = F[32,x]
F[35,x] = F[36,x]+F[37,x]+F[88,x]
F[36,x] = 0
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[49,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[1,x]+F[4,x]
F[43,x] = F[36,x]+F[44,x]+F[47,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[16,x]+F[46,x]
F[46,x] = F[17,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[11,x]+F[17,x]
F[49,x] = F[50,x]+F[71,x]
F[50,x] = F[36,x]+F[37,x]+F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[19,x]+F[53,x]
F[53,x] = F[36,x]+F[54,x]+F[63,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[61,x]
F[56,x] = F[4,x]+F[57,x]
F[57,x] = F[36,x]+F[58,x]+F[60,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[16,x]
F[60,x] = F[11,x]*F[4,x]
F[61,x] = F[62,x]+F[64,x]
F[62,x] = F[63,x]
F[63,x] = F[19,x]*F[4,x]
F[64,x] = 2*F[36,x]+F[65,x]+F[70,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[62,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[67,x]
F[70,x] = F[32,x]*F[4,x]
F[71,x] = 2*F[36,x]+F[72,x]+F[85,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[84,x]
F[74,x] = F[75,x]+F[82,x]
F[75,x] = F[36,x]+F[63,x]+F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[80,x]
F[78,x] = F[4,x]+F[79,x]
F[79,x] = F[36,x]+F[44,x]+F[60,x]
F[80,x] = F[75,x]+F[81,x]
F[81,x] = 2*F[36,x]+F[70,x]+F[72,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[74,x]
F[84,x] = F[82,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[32,x]+F[87,x]
F[87,x] = F[69,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[93,x]
F[90,x] = F[19,x]+F[91,x]
F[91,x] = F[36,x]+F[76,x]+F[92,x]
F[92,x] = F[4,x]*F[90,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[33,x]+F[36,x]+F[54,x]
F[95,x] = F[83,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_{18}\! \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_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \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_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{19}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{88}\! \left(x \right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{49}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{36}\! \left(x \right)+F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{16}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{17}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{71}\! \left(x \right)
F_{50}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \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_{19}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{36}\! \left(x \right)+F_{54}\! \left(x \right)+F_{63}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{61}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{36}\! \left(x \right)+F_{58}\! \left(x \right)+F_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{16}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{64}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{65}\! \left(x \right)+F_{70}\! \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_{62}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{72}\! \left(x \right)+F_{85}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{84}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{82}\! \left(x \right)
F_{75}\! \left(x \right) = F_{36}\! \left(x \right)+F_{63}\! \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_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{36}\! \left(x \right)+F_{44}\! \left(x \right)+F_{60}\! \left(x \right)
F_{80}\! \left(x \right) = F_{75}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{84}\! \left(x \right) = F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{32}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{69}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = F_{19}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{36}\! \left(x \right)+F_{76}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)+F_{54}\! \left(x \right)
F_{95}\! \left(x \right) = F_{83}\! \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_18(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_11(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_4(x))
Eq(F_17(x), F_15(x))
Eq(F_18(x), F_19(x) + F_35(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_27(x))
Eq(F_22(x), F_1(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_10(x) + F_26(x))
Eq(F_26(x), F_11(x))
Eq(F_27(x), F_19(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_19(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_31(x)*F_4(x))
Eq(F_34(x), F_32(x))
Eq(F_35(x), F_36(x) + F_37(x) + F_88(x))
Eq(F_36(x), 0)
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_49(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_1(x) + F_4(x))
Eq(F_43(x), F_36(x) + F_44(x) + F_47(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_16(x) + F_46(x))
Eq(F_46(x), F_17(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_11(x) + F_17(x))
Eq(F_49(x), F_50(x) + F_71(x))
Eq(F_50(x), F_36(x) + F_37(x) + F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_19(x) + F_53(x))
Eq(F_53(x), F_36(x) + F_54(x) + F_63(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_61(x))
Eq(F_56(x), F_4(x) + F_57(x))
Eq(F_57(x), F_36(x) + F_58(x) + F_60(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_16(x))
Eq(F_60(x), F_11(x)*F_4(x))
Eq(F_61(x), F_62(x) + F_64(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_19(x)*F_4(x))
Eq(F_64(x), 2*F_36(x) + F_65(x) + F_70(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_62(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_67(x))
Eq(F_70(x), F_32(x)*F_4(x))
Eq(F_71(x), 2*F_36(x) + F_72(x) + F_85(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_84(x))
Eq(F_74(x), F_75(x) + F_82(x))
Eq(F_75(x), F_36(x) + F_63(x) + F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_80(x))
Eq(F_78(x), F_4(x) + F_79(x))
Eq(F_79(x), F_36(x) + F_44(x) + F_60(x))
Eq(F_80(x), F_75(x) + F_81(x))
Eq(F_81(x), 2*F_36(x) + F_70(x) + F_72(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_74(x))
Eq(F_84(x), F_82(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_32(x) + F_87(x))
Eq(F_87(x), F_69(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_93(x))
Eq(F_90(x), F_19(x) + F_91(x))
Eq(F_91(x), F_36(x) + F_76(x) + F_92(x))
Eq(F_92(x), F_4(x)*F_90(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_33(x) + F_36(x) + F_54(x))
Eq(F_95(x), F_83(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": [0, 2, 3, 1], "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": [3, 1, 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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "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": [3, 1, 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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "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": [3, 1, 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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [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, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [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": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"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, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "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, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [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, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 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