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A140806 Expansion of x *(1+x) *(x^2+1) *(15*x^4+1) / ( (x^4-2*x^3+2*x^2+2*x+1) *(x^4+2*x^3+2*x^2-2*x+1) ). 0

%I

%S 1,1,1,1,1,1,1,1,-15,-15,-15,-15,209,209,209,209,-2911,-2911,-2911,

%T -2911,40545,40545,40545,40545,-564719,-564719,-564719,-564719,

%U 7865521,7865521,7865521,7865521,-109552575,-109552575,-109552575,-109552575,1525870529,1525870529,1525870529

%N Expansion of x *(1+x) *(x^2+1) *(15*x^4+1) / ( (x^4-2*x^3+2*x^2+2*x+1) *(x^4+2*x^3+2*x^2-2*x+1) ).

%C A Matrix Markov sequence based on the polynomial in the cubic elliptic invariant of A113922: characteristic polynomial x^8+14*x^4+1; Bezout matrix in the Mathematica code.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,-14,0,0,0,-1).

%F M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {-1, 0, 0, 0, -14, 0, 0, 0}}; v(n)=M.v(n-1): a(n)=v(n)( element 1).

%t M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {-1, 0, 0, 0, -14, 0, 0, 0}}; v[0] = {1, 1, 1, 1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[v[n][[1]], {n, 0, 50}]

%Y Cf. A113922.

%K uned,sign

%O 1,9

%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 15 2008

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)