0123_0132_0321_2103
Counting sequence:
1, 1, 2, 6, 20, 60, 162, 442, 1245, 3534, 9976, 28023, 78711, 221417, 623200, 1753637, 4933335, 13878117, 39043660, 109846204, 309040824, 869442525, 2446047425, 6881612750, 19360492934, 54468132584, 153238633940, 431115841674, 1212885351070, 3412287106405, 9600003213414, 27008295559448, 75984143390343, 213770989967243, 601415431771861, 1692000031269868, 4760210580186297, 13392201142622863, 37677125509641585, 105999437430726884, 298214913800915484, 838986856558738592, 2360374725994612937, 6640591331791334417, 18682395109073300970, 52560362409557993894, 147871388035990133164, 416015917646448551036, 1170403862666892178770, 3292771126394070227794, 9263761028702959447565, 26062324134530244460462, 73322782959173528170984, 206283617421326553159751, 580350732733689966342191, 1632737379704855624364401, 4593483217516251666053752, 12923136526351541139758861, 36357476400887792458584055, 102286785220112811844831453, 287769874765290847414200396, 809601168364296270447227084, 2277702113021493033005484648, 6408003247011326193546812565, 18028040356531128714125370673, 50719424845531852399900911766, 142692162086802345217309678438, 401444874089497630636711419168, 1129410225312145379823565522420, 3177441136675860364951378994042, 8939295882724652740639436998870, 25149485841458681161899851857493, 70754637321272875362831417399590, 199058491057187258156176467939944, 560023828290488354105268145456183, 1575550415294934471795425532933795, 4432595517790045011464783856880701, 12470500996729080621979391932422660, 35084048270426253725087321820235617, 98704169412636491979042622919918799, 277690675384539327144868354036016233, 781244719999127039387632618041394948, 2197925125434355184636053161203864972, 6183561607969681993989067699042743504, 17396604514451006961436013807911814657, 48942966500431931789558087903071954209, 137694339597855457145945607082186776402, 387384184346942308696101800370463873222, 1089852398583877718037648446942724783108, 3066150603699541066879610543375545712124, 8626195195590528921709223993624163774082, 24268619898398456869224124192327859753514, 68276441515490458783638311750193102153405, 192086426238264325553823721935154557928526, 540408877879450997538220478841602958641560, 1520366436140981134106539111439090258930903, 4277342943021852964076742918589097450792487, 12033719120146584927159786206114714991132345, 33855222223606881157738370570874868503780496, 95247035464780191320432448638152880585435125, 267964502046697225981271394284725650009913815
Generating function in Maple syntax:
-(x^4+3*x^3+x^2-1)/(4*x^10+16*x^9+21*x^8+8*x^7-8*x^6-12*x^5-6*x^4-5*x^3-2*x^2-x+1)
Generating function in latex syntax:
-\frac{x^{4}+3 x^{3}+x^{2}-1}{4 x^{10}+16 x^{9}+21 x^{8}+8 x^{7}-8 x^{6}-12 x^{5}-6 x^{4}-5 x^{3}-2 x^{2}-x +1}
Generating function in sympy syntax:
(-x**4 - 3*x**3 - x**2 + 1)/(4*x**10 + 16*x**9 + 21*x**8 + 8*x**7 - 8*x**6 - 12*x**5 - 6*x**4 - 5*x**3 - 2*x**2 - x + 1)
Implicit equation for the generating function in Maple syntax:
(4*x^10+16*x^9+21*x^8+8*x^7-8*x^6-12*x^5-6*x^4-5*x^3-2*x^2-x+1)*F(x)+x^4+3*x^3+x^2-1 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{10}+16 x^{9}+21 x^{8}+8 x^{7}-8 x^{6}-12 x^{5}-6 x^{4}-5 x^{3}-2 x^{2}-x +1\right) F \! \left(x \right)+x^{4}+3 x^{3}+x^{2}-1 = 0
Explicit closed form in Maple syntax:
-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+8)-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+8)-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+8)-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+8)-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+8)-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+8)-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+8)-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+8)-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+8)-31714115169909/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+8)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+7)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+7)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+7)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+7)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+7)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+7)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+7)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+7)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+7)-95219674867549/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+7)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+6)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+6)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+6)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+6)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+6)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+6)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+6)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+6)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+6)-250051898450109/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+6)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+5)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+5)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+5)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+5)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+5)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+5)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+5)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+5)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+5)+29948286076775/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+5)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+4)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+4)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+4)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+4)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+4)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+4)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+4)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+4)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+4)-37020065045133/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+4)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+3)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+3)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+3)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+3)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+3)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+3)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+3)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+3)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+3)-55089305377221/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+3)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+2)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+2)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+2)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+2)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+2)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+2)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+2)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+2)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+2)+38760982889421/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+2)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+1)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+1)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+1)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+1)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+1)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+1)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+1)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+1)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+1)+108562421801273/663040699080484*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n-1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n-1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n-1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n-1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n-1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n-1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n-1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n-1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n-1)+65559996125697/1326081398160968*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n-1)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n)+40468192057291/331520349540242*RootOf(4*_Z^10+16*_Z^9+21*_Z^8+8*_Z^7-8*_Z^6-12*_Z^5-6*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n)
Explicit closed form in latex syntax:
-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +8}}{331520349540242}-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +8}}{331520349540242}-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +8}}{331520349540242}-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +8}}{331520349540242}-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +8}}{331520349540242}-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +8}}{331520349540242}-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +8}}{331520349540242}-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +8}}{331520349540242}-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +8}}{331520349540242}-\frac{31714115169909 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n +8}}{331520349540242}-\frac{95219674867549 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +7}}{331520349540242}-\frac{95219674867549 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +7}}{331520349540242}-\frac{95219674867549 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +7}}{331520349540242}-\frac{95219674867549 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +7}}{331520349540242}-\frac{95219674867549 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +7}}{331520349540242}-\frac{95219674867549 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +7}}{331520349540242}-\frac{95219674867549 \mathit{RootOf}\! 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\left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +2}}{1326081398160968}+\frac{38760982889421 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n +2}}{1326081398160968}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{663040699080484}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{663040699080484}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{663040699080484}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{663040699080484}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{663040699080484}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{663040699080484}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{663040699080484}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{663040699080484}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +1}}{663040699080484}+\frac{108562421801273 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n +1}}{663040699080484}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{1326081398160968}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{1326081398160968}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{1326081398160968}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{1326081398160968}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{1326081398160968}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{1326081398160968}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{1326081398160968}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{1326081398160968}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n -1}}{1326081398160968}+\frac{65559996125697 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n -1}}{1326081398160968}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{331520349540242}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{331520349540242}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{331520349540242}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{331520349540242}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{331520349540242}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{331520349540242}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{331520349540242}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{331520349540242}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n}}{331520349540242}+\frac{40468192057291 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+21 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}-12 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n}}{331520349540242}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 60
a(6) = 162
a(7) = 442
a(8) = 1245
a(9) = 3534
a(n+10) = -4*a(n)-16*a(n+1)-21*a(n+2)-8*a(n+3)+8*a(n+4)+12*a(n+5)+6*a(n+6)+5*a(n+7)+2*a(n+8)+a(n+9), 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) = 60
a \! \left(6\right) = 162
a \! \left(7\right) = 442
a \! \left(8\right) = 1245
a \! \left(9\right) = 3534
a \! \left(n +10\right) = -4 a \! \left(n \right)-16 a \! \left(n +1\right)-21 a \! \left(n +2\right)-8 a \! \left(n +3\right)+8 a \! \left(n +4\right)+12 a \! \left(n +5\right)+6 a \! \left(n +6\right)+5 a \! \left(n +7\right)+2 a \! \left(n +8\right)+a \! \left(n +9\right), \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14812/
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[81,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[34,x]
F[23,x] = F[24,x]+F[7,x]
F[24,x] = F[15,x]+F[25,x]+F[28,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[18,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[16,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]*F[4,x]
F[34,x] = F[35,x]+F[48,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[2,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[2,x]*F[4,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[43,x]
F[43,x] = F[38,x]*F[4,x]
F[44,x] = 2*F[15,x]+F[45,x]+F[47,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[39,x]
F[47,x] = F[4,x]*F[42,x]
F[48,x] = 2*F[15,x]+F[49,x]+F[75,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[39,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[15,x]+F[55,x]+F[66,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[60,x]
F[57,x] = F[12,x]+F[58,x]
F[58,x] = F[15,x]+F[25,x]+F[59,x]
F[59,x] = F[11,x]*F[4,x]
F[60,x] = F[42,x]+F[61,x]
F[61,x] = 2*F[15,x]+F[49,x]+F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[54,x]+F[64,x]
F[64,x] = 2*F[15,x]+F[53,x]+F[65,x]
F[65,x] = F[4,x]*F[51,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[2,x]+F[68,x]
F[68,x] = F[15,x]+F[40,x]+F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[73,x]
F[71,x] = F[4,x]+F[72,x]
F[72,x] = F[15,x]+F[18,x]+F[25,x]
F[73,x] = F[39,x]+F[74,x]
F[74,x] = 2*F[15,x]+F[49,x]+F[53,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[63,x]+F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[65,x]
F[79,x] = F[80,x]
F[80,x] = F[4,x]*F[78,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[67,x]+F[83,x]
F[83,x] = F[54,x]+F[84,x]
F[84,x] = F[15,x]+F[53,x]+F[65,x]+F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[91,x]
F[87,x] = F[14,x]+F[88,x]
F[88,x] = F[15,x]+F[33,x]+F[89,x]+F[90,x]
F[89,x] = 0
F[90,x] = F[27,x]*F[4,x]
F[91,x] = F[44,x]+F[92,x]
F[92,x] = 2*F[15,x]+F[80,x]+F[93,x]+F[94,x]
F[93,x] = 0
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[53,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_{81}\! \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_{34}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{16}\! \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_{35}\! \left(x \right)+F_{48}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{39}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{49}\! \left(x \right)+F_{75}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{39}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)+F_{55}\! \left(x \right)+F_{66}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{60}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{60}\! \left(x \right) = F_{42}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{49}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{54}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{53}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right)+F_{40}\! \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_{73}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{73}\! \left(x \right) = F_{39}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{63}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{65}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{67}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{54}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{15}\! \left(x \right)+F_{53}\! \left(x \right)+F_{65}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{91}\! \left(x \right)
F_{87}\! \left(x \right) = F_{14}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)+F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = 0
F_{90}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{91}\! \left(x \right) = F_{44}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{80}\! \left(x \right)+F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = 0
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{53}\! \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_81(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_34(x))
Eq(F_23(x), F_24(x) + F_7(x))
Eq(F_24(x), F_15(x) + F_25(x) + F_28(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_18(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_16(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_31(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_48(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_2(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_2(x)*F_4(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_38(x)*F_4(x))
Eq(F_44(x), 2*F_15(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_39(x))
Eq(F_47(x), F_4(x)*F_42(x))
Eq(F_48(x), 2*F_15(x) + F_49(x) + F_75(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_39(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_15(x) + F_55(x) + F_66(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_60(x))
Eq(F_57(x), F_12(x) + F_58(x))
Eq(F_58(x), F_15(x) + F_25(x) + F_59(x))
Eq(F_59(x), F_11(x)*F_4(x))
Eq(F_60(x), F_42(x) + F_61(x))
Eq(F_61(x), 2*F_15(x) + F_49(x) + F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_54(x) + F_64(x))
Eq(F_64(x), 2*F_15(x) + F_53(x) + F_65(x))
Eq(F_65(x), F_4(x)*F_51(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_2(x) + F_68(x))
Eq(F_68(x), F_15(x) + F_40(x) + F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_73(x))
Eq(F_71(x), F_4(x) + F_72(x))
Eq(F_72(x), F_15(x) + F_18(x) + F_25(x))
Eq(F_73(x), F_39(x) + F_74(x))
Eq(F_74(x), 2*F_15(x) + F_49(x) + F_53(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_63(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_65(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_4(x)*F_78(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_67(x) + F_83(x))
Eq(F_83(x), F_54(x) + F_84(x))
Eq(F_84(x), F_15(x) + F_53(x) + F_65(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_91(x))
Eq(F_87(x), F_14(x) + F_88(x))
Eq(F_88(x), F_15(x) + F_33(x) + F_89(x) + F_90(x))
Eq(F_89(x), 0)
Eq(F_90(x), F_27(x)*F_4(x))
Eq(F_91(x), F_44(x) + F_92(x))
Eq(F_92(x), 2*F_15(x) + F_80(x) + F_93(x) + F_94(x))
Eq(F_93(x), 0)
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_53(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": [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, 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": [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, 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": [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, 1, 2], "pos": [[0, 1], [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, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 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": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2], [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, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 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, 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": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": 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