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Search: id:A107476
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| A107476 |
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Vector Matrix Markov of real valued characteristic polynomial:-x^6+6*x^5+4*x^4-24*x^3+6*x^2+4*x-1. |
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+0
1
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| 1, 1, 2, 3, 5, 4, 13, 157, 1050, 6575, 39949, 241792, 1459663, 8809863, 53159766, 320770109, 1935508203, 11678751308, 70468796429, 425204036789, 2565652344946, 15480972873087, 93411142010973, 563636507934624
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OFFSET
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0,3
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COMMENT
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After m=3 this polynomial doesn't factor. Factor[Det[M - x*IdentityMatrix[6]]] Real Roots: {{x -> -2.05681}, {x -> -0.405288}, {x -> 0.242751}, {x -> 0.480326}, {x -> 1.70508}, {x -> 6.03393}}
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FORMULA
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m=4 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 + 2), -m*(m + 2), m, (m + 2)}} v[n]=M.v[n-1] a(n) = v[n][[1]]
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MATHEMATICA
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m=4 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 + 2), -m*(m + 2), m, (m + 2)}} v[0] = {0, 1, 1, 2, 3, 5} 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: A101409 A131401 A061446 this_sequence A094140 A119745 A095753
Adjacent sequences: A107473 A107474 A107475 this_sequence A107477 A107478 A107479
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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), May 27 2005
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