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Search: id:A130636
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| A130636 |
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A vector matrix Markov doubly recursive sequence with characteristic polynomial: -1 - n x + x^4 and matrix: M(n)={{0, 0, n, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}. |
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+0
1
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| 0, 1, 0, 0, 4, 1, 0, 28, 12, 1, 280, 160, 24, 3641, 2520, 520, 58280, 46481, 11880, 1107840, 987900, 295961, 24384360, 23829540, 8090964, 609904961, 643952400, 242285568, 17085429872, 19284524561, 7912519440
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Determinants are all -1. The toral inverses appear to be Pisot: f[x_] = CharacteristicPolynomial[M[n], x] Table[NSolve[x^4*f[1/x] == 0, x], {n, 0, 10}] Table[Expand[x^4*f[1/x]], {n, 0, 10}]
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FORMULA
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M(0) = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 1}}; M(n)={{0, 0, n, 1}, {1, 0, 0, 0}, {0, 1, 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, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 1}}; M[n_] := {{0, 0, n, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}; v[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: A007789 A081114 A069018 this_sequence A117414 A085639 A135302
Adjacent sequences: A130633 A130634 A130635 this_sequence A130637 A130638 A130639
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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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