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Search: id:A123020
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| A123020 |
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Let M = {{1, 1, 0, 0}, {1, 2, 1, 1}, {0, 1, 2, 1}, {0, 0, 1, 2}}, v[1] = {1, 0, 0, 0}, v[n] = M.v[n - 1]. Then a(n) = v[n][[1]]. |
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+0
1
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| 1, 1, 2, 5, 14, 43, 142, 493, 1766, 6443, 23750, 88045, 327406, 1219531, 4546622, 16958765, 63272054, 236096683, 881049142, 3287968813, 12270563966, 45793762763, 170903438510, 637817894125, 2380363943686, 8883629492011
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A 4 X 4 vector Markov chain with characteristic polynomial 2 - 11 x + 15 x^2 - 7 x^3 + x^4.
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LINKS
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Eric Weisstein's World of Mathematics, Morgan-Voyce Polynomials
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MATHEMATICA
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M = {{1, 1, 0, 0}, {1, 2, 1, 1}, {0, 1, 2, 1}, {0, 0, 1, 2}} v[1] = {1, 0, 0, 0} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
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CROSSREFS
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Cf. A001519, A080937.
Sequence in context: A149880 A066351 A029889 this_sequence A005317 A126566 A112808
Adjacent sequences: A123017 A123018 A123019 this_sequence A123021 A123022 A123023
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 24 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 13 2007
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