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A121872 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. 0
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; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..34.

FORMULA

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))

EXAMPLE

5

13, 41

34, 153, 436

89, 571, 2089, 5741

233, 2131, 10009, 33461, 90481

MATHEMATICA

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]

CROSSREFS

Cf. A094954, A162997

Sequence in context: A054856 A261057 A283456 * A228922 A025490 A216824

Adjacent sequences:  A121869 A121870 A121871 * A121873 A121874 A121875

KEYWORD

nonn,easy,tabl,uned

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 09 2006

STATUS

approved

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Last modified May 26 23:51 EDT 2019. Contains 323597 sequences. (Running on oeis4.)