A163867 a(n) = a(floor(n/3)) + a(floor(2*n/3)); a(0) = 1.

1, 2, 3, 5, 5, 7, 8, 8, 10, 13, 13, 13, 15, 15, 18, 20, 20, 20, 23, 23, 23, 26, 26, 28, 30, 30, 30, 36, 36, 36, 36, 36, 39, 39, 39, 41, 45, 45, 45, 45, 45, 51, 54, 54, 54, 56, 56, 56, 59, 59, 59, 59, 59, 61, 68, 68, 68, 68, 68, 68, 68, 68, 74, 80, 80, 80, 80, 80, 82, 84, 84, 84

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Sungjin Kim, Mathematics Stack Exchange Question 3051676 (showing a(n)/n converges).

Formula

G.f. g(x) satisfies g(x) = -1 + (1 + x + x^2) g(x^3) + (1 + x^(1/2) + x) g(x^(3/2))/2 + (1 - x^(1/2) + x) g(-x^(3/2))/2. - Robert Israel, Apr 22 2016

Maple

a:= proc(n) option remember; procname(floor(n/3)) + procname(floor(2*n/3)) end proc:
a(0):= 1:
seq(a(n), n=0..100); # Robert Israel, Apr 22 2016

Mathematica

a[0]=1; a[n_]:=a[n]=a[Floor[n/3]]+a[Floor[(2n)/3]]; Array[a, 80, 0] (* Harvey P. Dale, Jun 08 2018 *)

Prog

(PARI) a(n)={if(n==0, 1, a(n\3) + a(2*n\3))} \\ Andrew Howroyd, Feb 27 2018

Crossrefs

Sequence in context: A323185 A168065 A077724 * A077381 A225636 A023838

Adjacent sequences: A163864 A163865 A163866 * A163868 A163869 A163870

Keyword

nonn

Author

Reinhard Zumkeller, Aug 06 2009

Status

approved