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A140806
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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) ).
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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; internal format)
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OFFSET
| 1,9
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COMMENTS
| A Matrix Markov sequence based on the polynomial in the cubic elliptic invariant of A113922: characteristic polynomial x^8+14*x64+1; Bezout matrix in the Mathematica code.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,-14,0,0,0,-1).
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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): a9n)=v(n)( element 1).
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MATHEMATICA
| = {{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}]
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CROSSREFS
| Cf. A113922.
Sequence in context: A173430 A010854 A003884 * A085321 A003890 A040211
Adjacent sequences: A140803 A140804 A140805 * A140807 A140808 A140809
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KEYWORD
| uned,sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 15 2008
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