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Search: id:A107401
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| A107401 |
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Real root quintic vector Matrix Markov sequence m=4. |
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+0
1
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| 0, 1, 1, 2, 3, 8, 10, 31, 36, 117, 133, 438, 495, 1636, 1846, 6107, 6888, 22793, 25705, 85066, 95931, 317472, 358018, 1184823, 1336140, 4421821, 4986541, 16502462, 18610023, 61588028, 69453550, 229849651, 259204176, 857810577, 967363153
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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m=3 gives a Fibonacci. Real Roots are: {{x -> -1.93185}, {x -> -1.}, {x -> -0.517638}, {x -> 0.517638}, {x -> 1.93185}}
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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, -1, m, m, -1}} v[n]=M.v[n-1] a(n) = v[n][[1]]
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MATHEMATICA
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n = 4 M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {-1, -1, m, m, -1}} Expand[Det[M - x*IdentityMatrix[5]]] NSolve[Det[M - x*IdentityMatrix[5]] == 0, x] v[1] = {0, 1, 1, 2, 3} digits = 50 v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, digits}]
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CROSSREFS
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Sequence in context: A138880 A063474 A025562 this_sequence A121989 A010786 A005727
Adjacent sequences: A107398 A107399 A107400 this_sequence A107402 A107403 A107404
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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 25 2005
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