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

1,5

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]

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000045, A001622.

Sequence in context: A268823 A046877 A067587 * A120476 A069159 A306389

Adjacent sequences: A198256 A198257 A198258 * A198260 A198261 A198262

Keyword

nonn

Author

Benoit Cloitre, Oct 22 2011

Status

approved