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Search: id:A107389
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| A107389 |
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A quartic Fibonacci type alternating / chaotic vector Markov sequence of a quartic characteristic: x^4+5*x^2-5*x-1:for m=5. |
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2
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| 0, 1, 1, 2, 5, 31, 144, 697, 3335, 15986, 76589, 366967, 1758240, 8424241, 40362959, 193390562, 926589845, 4439558671, 21271203504, 101916458857, 488311090775, 2339638995026, 11209883884349, 53709780426727, 257339018249280, 1232985310819681, 5907587535849119, 28304952368425922, 135617174306280485, 649780919162976511, 3113287421508602064, 14916656188380033817, 71469993520391567015, 342433311413577801266, 1640696563547497439309, 7861049506323909395287, 37664550968072049537120, 180461705334036338290321, 864643975702109641914479, 4142758173176511871282082, 19849146890180449714495925, 95102976277725736701197551, 455665734498448233791491824, 2183225696214515432256261577, 10460462746574128927489816055, 50119088036656129205192818706, 240134977436706517098474277469, 1150555799146876456287178568647, 5512644018297675764337418565760, 26412664292341502365399914260161
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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m=5 M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, -m}}; v[n] = M.v[n - 1] a(n) =Abs[v[n][[1]]]
m=5; M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, -m}}; v[n] = M.v[n - 1]; a(n) =Abs[v[n][[1]]]
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MATHEMATICA
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m = 5 M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, - m) Expand[Det[M - x*IdentityMatrix[4]]] (*-1 - 5 x + 5 x^3 + x^4*) NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M . v[n - 1] digits = 50; aa = Table[Abs[v[n][[1]], {n, 1, digits}]
Clear[M, m, v, aa] (*A107389*)m = 5; M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, - m}}; Expand[Det[M - x*IdentityMatrix[4]]] ; NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] ; v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M . v[n - 1]; digits = 50; aa = Table[Abs[v[n][[1]]], {n, 1, digits}]
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CROSSREFS
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Adjacent sequences: A107386 A107387 A107388 this_sequence A107390 A107391 A107392
Sequence in context: A127298 A000133 A059086 this_sequence A077483 A119242 A068145
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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 24 2005, corrected Sep 04 2008
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