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A117792
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First entry of the vector (M^n)w, where M is the 6x6 matrix [[0, 1, 0, 0, 0, 0, ], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, -1, 0, 1, 1]] and w is the column vector [0, 1, 1, 2, 3, 5].
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0
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0, 1, 1, 2, 3, 5, 7, 11, 16, 24, 36, 54, 81, 122, 183, 275, 413, 620, 931, 1398, 2099, 3152, 4733, 7107, 10672, 16025, 24063, 36133, 54257, 81472, 122338, 183702, 275846, 414209, 621974, 933953, 1402419, 2105865, 3162156, 4748277, 7129988, 10706353
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..41.
Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,0,1).
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FORMULA
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G.f.: -x*(1+x^4) / ( -1+x+x^2-x^4+x^6 ). - R. J. Mathar, Jul 14 2014
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MAPLE
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with(linalg): M:=matrix(6, 6, [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0, 1, 1]): w[0]:=matrix(6, 1, [0, 1, 1, 2, 3, 5]): for n from 1 to 45 do w[n]:=multiply(M, w[n-1]) od: seq(w[n][1, 1], n=0..45);
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MATHEMATICA
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M = {{0, 1, 0, 0, 0, 0 }, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {1, 0, -1, 0, 1, 1}}; w[1] = {0, 1, 1, 2, 3, 5}; w[n_] := w[n] = M.w[n - 1] Table[w[n][[1]], {n, 1, 25}]
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CROSSREFS
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Sequence in context: A333589 A112088 A333588 * A154888 A271485 A018057
Adjacent sequences: A117789 A117790 A117791 * A117793 A117794 A117795
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula, Apr 15 2006
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EXTENSIONS
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Edited by N. J. A. Sloane, Apr 30 2006
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STATUS
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approved
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