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A109543
a(n) = a(n-1) + a(n-3) + a(n-5), with a(1..5) = 1.
10
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
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.
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
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Jun 20 2005
STATUS
approved