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Search: id:A121872
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| A121872 |
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Binet-like triangular array based on Silver means of the second kind: a[n] = m*a[n - 1] - a[n - 2],m held as a constant. |
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+0
1
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| 5, 13, 41, 34, 153, 436, 89, 571, 2089, 5741, 233, 2131, 10009, 33461, 90481, 610, 7953, 47956, 195025, 620166, 1663585, 1597, 29681, 229771, 1136689, 4250681, 13097377, 34988311, 4181, 110771, 1100899, 6625109, 29134601, 103115431
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n,m) = (1/Sqrt[ -4 + m^2])*(2^(-1 - n) ((-2 + m) (m - Sqrt[ -4 + m^2])^n + Sqrt[ -4 + m^2] (m - Sqrt[ -4 + m^2])^n - (-2 + m) (m + Sqrt[ -4 + m^2])^n + Sqrt[ -4 + m^2] (m + Sqrt[ -4 + m^2])^n))
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EXAMPLE
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5
13, 41
34, 153, 436
89, 571, 2089, 5741
233, 2131, 10009, 33461, 90481
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MATHEMATICA
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f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == m*a[n - 1] - a[n - 2], a[0] == 1, a[1] == 1}, a[n], n][[1]] // FullSimplify] T[n_, m_] = (1/Sqrt[ -4 + m^2])*(2^(-1 - n) ((-2 + m) (m - Sqrt[ -4 + m^2])^n + Sqrt[ -4 + m^2] (m - Sqrt[ -4 + m^2])^n - (-2 + m) (m + Sqrt[ -4 + m^2])^n + Sqrt[ -4 + m^2] (m + Sqrt[ -4 + m^2])^n)) a = Delete[Delete[ Table[Rationalize[N[ Table[T[n, m], {m, 3, n}], 100], 0], {n, 1, 10}], 2], 1]
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CROSSREFS
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Sequence in context: A077919 A026069 A054856 this_sequence A025490 A087938 A103729
Adjacent sequences: A121869 A121870 A121871 this_sequence A121873 A121874 A121875
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 09 2006
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