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Search: id:A107451
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| A107451 |
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Let m = 5 and set 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, m, (m + 1), -m*(m + 1), -m, (m + 2)}}. Let v[0] = {0, 1, 1, 2, 3, 5}, v[n] = M.v[n - 1]. Then a = Abs[v[n][[1]]. |
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+0
1
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| 1, 1, 2, 3, 5, 29, 302, 2092, 12221, 66179, 341350, 1705958, 8333070, 40017287, 189643693, 889303635, 4134575230, 19086260759, 87581455636, 399845651745, 1817488787127, 8230050719153, 37144327008467, 167153266777585
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OFFSET
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0,3
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COMMENT
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Based on a Markov chain with characteristic polynomial 1 - m* x - (m + 1) *x^2 + m*(m + 1)* x^3 + m* x^4 - (m + 2)* x^5 + x^6 with m=5.
This is a doubled Bombieri polynomial with real roots {{x -> -1.64378}, {x -> -0.425321}, {x -> 0.201585}, {x -> 0.395849}, {x -> 4.10318}, {x -> 4.36848}}. The base vector is Fibonacci-like.
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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, m, (m + 1), -m*(m + 1), -m, (m + 2)}} Det[M - x*IdentityMatrix[6]] m = 5; NSolve[Det[M - x*IdentityMatrix[6]] == 0, x] v[0] = {0, 1, 1, 2, 3, 5} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}]
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CROSSREFS
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Sequence in context: A019400 A084599 A062167 this_sequence A093490 A073309 A110389
Adjacent sequences: A107448 A107449 A107450 this_sequence A107452 A107453 A107454
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 26 2005
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 16 2007
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