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Search: id:A107840
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| A107840 |
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A quadratic sequence with limit of the golden mean squared and characteristic polynomial: x^4+3*x^2-3*x-1. |
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+0
1
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| 1, 1, 1, 0, 4, 8, 25, 63, 169, 440, 1156, 3024, 7921, 20735, 54289, 142128, 372100, 974168, 2550409, 6677055, 17480761, 45765224, 119814916, 313679520, 821223649, 2149991423, 5628750625, 14736260448, 38580030724, 101003831720
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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a[n]/a[n-1]-->1+(Sqrt[5]+1)/2
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FORMULA
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F[n] = -3*F[n - 1] + 3*F[n - 3] + F[n - 4] a(n) = Abs[F[n]]
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MATHEMATICA
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(* method one*) F[1] = 1; F[2] = 1; F[3] = 1; F[4] = 0; F[n__] := F[n] = -3*F[n - 1] + 3*F[n - 3] + F[n - 4] a = Table[Abs[F[n]], {n, 1, 50}] an = Table[N[a[[n]]/a[[n - 1]]], {n, 6, 25}] (* method two*) M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 3, 0, -3}} v[1] = {1, 1, 1, 0} v[n_] := v[n] = M.v[n - 1] a0 = Table[Abs[v[n][[1]]], {n, 1, 50}] an = Table[N[a0[[n]]/a0[[n - 1]]], {n, 6, 25}] Det[M - x*IdentityMatrix[4]]
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CROSSREFS
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Adjacent sequences: A107837 A107838 A107839 this_sequence A107841 A107842 A107843
Sequence in context: A131637 A068367 A000964 this_sequence A046736 A074188 A126733
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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), Jun 12 2005
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