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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
 1, 1, 1, 1, 1, 1, 1, 1, -15, -15, -15, -15, 209, 209, 209, 209, -2911, -2911, -2911, -2911, 40545, 40545, 40545, 40545, -564719, -564719, -564719, -564719, 7865521, 7865521, 7865521, 7865521, -109552575, -109552575, -109552575, -109552575, 1525870529, 1525870529, 1525870529 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS 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. LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,-14,0,0,0,-1). FORMULA 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). MATHEMATICA 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}] CROSSREFS Cf. A113922. Sequence in context: A010854 A003884 A225917 * A085321 A239315 A003890 Adjacent sequences:  A140803 A140804 A140805 * A140807 A140808 A140809 KEYWORD uned,sign AUTHOR Roger L. Bagula and Gary W. Adamson, Jul 15 2008 STATUS approved

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)