A132915 a(0)=0; a(1)=1; a(n) = Sum_{k=1..[sqrt(n)]} a(n-k) for n>=2.

0, 1, 1, 1, 2, 3, 5, 8, 13, 26, 47, 86, 159, 292, 537, 988, 1976, 3793, 7294, 14051, 27114, 52252, 100711, 194128, 374205, 748410, 1469706, 2887160, 5673609, 11153090, 21931975, 43115540, 84761374, 166635588, 327597567, 644042044, 1288084088, 2554236201, 5065356862

Offset

0,5

Comments

Lim n->infinity {a(n+1)/a(n)} = 2. Contrast with Fibonacci sequence. Also a(n+1)/a(n) = 2 iff n+1 is square.

Links

Table of n, a(n) for n=0..38.

Formula

a(n) = Sum_{k=1..[sqrt(n)]} a(n-k), for n>=2; a(0)=0; a(1)=1.

Example

a(9) = a(6) + a(7) + a(8) = 5 + 8 + 13 = 26.

Maple

a:= proc(n) option remember; `if`(n<2, n,
      add(a(n-j), j=1..floor(sqrt(n))))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Feb 04 2026

Crossrefs

Cf. A000045, A000196, A132916.

Sequence in context: A336604 A024318 A324738 * A030036 A115212 A158083

Adjacent sequences: A132912 A132913 A132914 * A132916 A132917 A132918

Keyword

nonn

Author

Rick L. Shepherd, Sep 04 2007

Status

approved