Voozh

A298356

a(n) = a(n-1) + a(n-2) + a([n/2]) + a([n/3]) + ... + a([n/n]), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 4, 8, 16, 32, 57, 103, 178, 308, 514, 874, 1441, 2394, 3926, 6462, 10531, 17231, 28001, 45614, 74026, 120258, 194903, 316210, 512171, 830007, 1343883, 2176578, 3523150, 5704107, 9231637, 14942711, 24181525, 39135483, 63328289, 102482212, 165828942

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OFFSET

0,4

COMMENTS

a(n)/a(n-1) -> (1 + sqrt(5))/2, the golden ratio (A001622), so that (a(n)) has the growth rate of the Fibonacci numbers (A000045). See A298338 for a guide to related sequences.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

MATHEMATICA

a[0] = 1; a[1] = 1; a[2] = 1;

a[n_] := a[n] = a[n - 1] + a[n - 2] + Sum[a[Floor[n/k]], {k, 2, n}];

Table[a[n], {n, 0, 30}] (* A298356 *)

PROG

(Python)

from functools import lru_cache

@lru_cache(maxsize=None)

def A298356(n):

if n <= 2: