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Search: id:A130637
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| A130637 |
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A vector matrix Markov doubly recursive sequence with characteristic polynomial: 1 + n x^3 - x^5 and matrix: M(n)={{0, n, 0, 0, 1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}. |
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+0
1
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| 0, 1, 0, 3, 0, 15, 1, 105, 11, 945, 125, 10396, 1605, 135159, 23415, 2027510, 385036, 34469275, 7065807, 654939640, 143343650, 13754117476, 3188029575, 316351767755, 77167649440, 7908937537525, 2020113002916, 213544501542750
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OFFSET
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1,4
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COMMENT
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Determinants are all 1.
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FORMULA
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M(0) ={{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 0, 1, 0, 0}};; M(n)={{0, n, 0, 0, 1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}; v(n)=M(n).v(n-1) a(n) = v(n)[[1]]
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MATHEMATICA
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M[0] = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 0, 1, 0, 0}}; M[n_] := {{0, n, 0, 0, 1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}; v[0] = {0, 0, 0, 0, 1}; v[n_] := v[n] = M[n].v[n - 1]; a = Table[v[n][[1]], {n, 0, 30}]
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CROSSREFS
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Sequence in context: A065121 A138540 A123023 this_sequence A054882 A086479 A091000
Adjacent sequences: A130634 A130635 A130636 this_sequence A130638 A130639 A130640
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 19 2007
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