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

Author

Roger L. Bagula, Jun 20 2005

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 - x^3-x^4)/(1-x-x^3-x^5))); // G. C. Greubel, Nov 03 2018

Mathematica

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

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

Formula

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