A109543 a(n) = a(n-1) + a(n-3) + a(n-5), with a(1..5) = 1.

1, 1, 1, 1, 1, 3, 5, 7, 11, 17, 27, 43, 67, 105, 165, 259, 407, 639, 1003, 1575, 2473, 3883, 6097, 9573, 15031, 23601, 37057, 58185, 91359, 143447, 225233, 353649, 555281, 871873, 1368969, 2149483, 3375005, 5299255, 8320611, 13064585, 20513323, 32208939

Offset

0,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Peter Borwein and Kevin G. Hare, Some computations on Pisot and Salem numbers, 2000, table 1, p. 7.

Peter Borwein and Kevin G. Hare, Some computations on the spectra of Pisot and Salem numbers, Math. Comp. 71 (2002), 767-780.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,1).

Formula

G.f.: (1 - x^3 - x^4) / (1 - x - x^3 - x^5). - Colin Barker, Dec 17 2017

Mathematica

LinearRecurrence[{1, 0, 1, 0, 1}, {1, 1, 1, 1, 1}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2012 *)

Prog

(PARI) Vec((1 - x^3 - x^4) / (1 - x - x^3 - x^5) + O(x^50)) \\ Colin Barker, Dec 17 2017
(PARI) my(p=Mod('x, 'x^5-'x^4-'x^2-1)); a(n) = vecsum(Vec(lift(p^n))); \\ Kevin Ryde, Jan 15 2021
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 - x^3-x^4)/(1-x-x^3-x^5))); // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A107479, A107480, A109538, A109544, A114749, A125950, A130844, A143335, A147851.

Sequence in context: A152999 A024967 A135246 * A229168 A248714 A091567

Adjacent sequences: A109540 A109541 A109542 * A109544 A109545 A109546

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 20 2005

Status

approved