A198259 a(n) = Sum_{k=1..n} F(n mod k) where F = A000045, the Fibonacci numbers.

0, 0, 1, 1, 3, 2, 6, 5, 9, 9, 17, 13, 26, 26, 39, 39, 66, 61, 104, 102, 156, 162, 265, 249, 405, 419, 646, 652, 1059, 1031, 1676, 1696, 2660, 2705, 4362, 4283, 6937, 7039, 11159, 11206, 18138, 17998, 29130, 29325, 46805, 47075, 76171, 75713, 122502, 123123

Offset: 1

Author

Benoit Cloitre, Oct 22 2011

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Benoit Cloitre, An asymptotic formula for sum_{k=1..n}x^(n modk) [broken link]

Crossrefs

Cf. A000045, A001622.

Programs

Haskell

a198259 n = sum $ map (a000045 . (mod n)) [1..n]
-- Reinhard Zumkeller, Oct 22 2011

Mathematica

a[n_] := Sum[Fibonacci[Mod[n, k]], {k, 1, n}]; Array[a, 50] (* Amiram Eldar, May 24 2025 *)

Formula

a(n) is asymptotic to (1/10)*(5+sqrt(5))*phi^ceiling(n/2) where phi = (1+sqrt(5))/2.