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Search: id:A114749
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| A114749 |
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Vector Markov sequence of quartic characteristic Pascal-Salem polynomial x^5-(x+1)^4. |
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1
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| 0, 1, 1, 2, 3, 21, 50, 161, 501, 1532, 4723, 14551, 44800, 137971, 424901, 1308512, 4029693, 12409831, 38217250, 117693681, 362448951, 1116196192, 3437432913, 10585903361, 32600301650, 100395746291
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The first three of the sequence of polynomials: x^n-(x+1)^(n-1) are Pisots, this one with two unitary absolute values is Salem r = Abs[Table[x /. NSolve[Det[M - IdentityMatrix[5]*x] == 0, x][[n]], {n, 1, 5}]] gives:{0.56984, 0.56984, 1., 1., 3.0796}
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FORMULA
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M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 4, 6, 4, 1}}; w[0] = {0, 1, 1, 2, 3}; w[n_] := w[n] = M.w[n - 1] a(n) = w[n][[1]]
G.f.:x*(9*x^3+3*x^2-1)/((x^2+x+1)*(x^3+3*x^2+2*x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]
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MATHEMATICA
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M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 4, 6, 4, 1}}; w[0] = {0, 1, 1, 2, 3}; w[n_] := w[n] = M.w[n - 1] a = Flatten[Table[w[n][[1]], {n, 0, 25}]]
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CROSSREFS
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Sequence in context: A124447 A024765 A090122 this_sequence A141458 A080670 A073647
Adjacent sequences: A114746 A114747 A114748 this_sequence A114750 A114751 A114752
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Feb 18 2006
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