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Search: id:A015442
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| A015442 |
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Generalized Fibonacci numbers: a(n) = a(n-1) + 7 a(n-2), a(0)=0, a(1)=1. |
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+0
5
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| 0, 1, 1, 8, 15, 71, 176, 673, 1905, 6616, 19951, 66263, 205920, 669761, 2111201, 6799528, 21577935, 69174631, 220220176, 704442593, 2245983825, 7177081976, 22898968751, 73138542583, 233431323840, 745401121921, 2379420388801
(list; graph; listen)
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OFFSET
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0,4
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LINKS
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Joerg Arndt, Fxtbook
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FORMULA
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O.g.f.: x^2/(1-x-7x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 06 2008
a(n)={[ (1+sqrt(29))/2 ]^(n+1) - [ (1-sqrt(29))/2 ]^(n+1)}/sqrt(29).
Also a(n) = 8*a(n-2)+7*a(n-3) with characteristic polynomial x^3-8*x-7. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 30 2007.
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MATHEMATICA
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(* Mma programs from R. L. Bagula *)
(* recursion *) A15442[0] := 0; A15442[1] := 1; A15442[ 2] := 1; A15442[n_] := A15442[n] = 8*A15442[n - 2] + 7*A15442[n - 3]; Table[A15442[n], {n, 0, 25}]
(* matrix representation *) mat15442 = {{0, 1, 0}, {0, 0, 1}, {7, 8, 0}}; w15442[ 0] = {0, 1, 1}; w15442[n_] := w15442[n] = mat15442.w15442[n - 1]; Table[w15442[n][[1]], {n, 0, 25}]
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CROSSREFS
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Cf. A015440, A015441.
Adjacent sequences: A015439 A015440 A015441 this_sequence A015443 A015444 A015445
Sequence in context: A118526 A037377 A048732 this_sequence A110294 A110459 A132374
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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