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Search: id:A107477
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| A107477 |
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Vector Matrix Markov of real valued characteristic polynomial:-x^6+7*x^5+5*x^4-35*x^3+7*x^2+5*x-1. |
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+0
1
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| 1, 1, 2, 3, 5, 8, 118, 1011, 7339, 52332, 368505, 2591989, 18211138, 127942244, 898765639, 6313614979, 44351223914, 311553904337, 2188569785219, 15374026372032, 107997774755178, 758650932498691, 5329287885039911
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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 -> -2.28425}, {x -> -0.375048}, {x -> 0.197354}, {x -> 0.4167}, {x ->2.02056}, {x -> 7.02469}}
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FORMULA
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m=5 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=5 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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Adjacent sequences: A107474 A107475 A107476 this_sequence A107478 A107479 A107480
Sequence in context: A068500 A042667 A120495 this_sequence A064358 A109736 A119628
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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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