A033499 a(n) = a(n-1) + a(round(2*(n-1)/3)) + a(round((n-1)/3)) with a(1)=a(2)=1.

1, 1, 3, 5, 9, 13, 19, 29, 41, 57, 79, 103, 137, 183, 233, 299, 387, 479, 595, 745, 901, 1103, 1355, 1617, 1945, 2361, 2789, 3309, 3945, 4597, 5399, 6357, 7337, 8519, 9953, 11411, 13131, 15179, 17261, 19759, 22685, 25657, 29149, 33277, 37455, 42285, 47917, 53615, 60271, 67907, 75631

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Maple

A033499:= proc(n) option remember; if n <= 2 then 1 else A033499(n-1) + A033499(round(2*(n-1)/3)) + A033499(round((n-1)/3)); fi; end;

Mathematica

a[n_]:= a[n]= If[n<3, 1, a[n-1] +a[Round[2*(n-1)/3]] +a[Round[(n-1)/3]]]; Table[a[n], {n, 55}] (* G. C. Greubel, Oct 14 2019 *)

Prog

(PARI) a(n) = if(n<3, 1, a(n-1)+a(round(2*(n-1)/3)) +a(round((n-1)/3)) );
vector(55, n, a(n) ) \\ G. C. Greubel, Oct 14 2019
(Magma) a:= func< n | n lt 3 select 1 else Self(n-1) + Self(Round(2*(n-1)/3)) + Self(Round((n-1)/3)) >;
[a(n): n in [1..55]]; // G. C. Greubel, Oct 14 2019
(Sage)
@CachedFunction
def a(n):
    if (n<3): return 1
    else: return a(n-1) +a(round(2*(n-1)/3)) +a(round((n-1)/3))
[a(n) for n in (1..55)] # G. C. Greubel, Oct 14 2019

Crossrefs

Cf. A033498, A033500.

Sequence in context: A118026 A248956 A108754 * A267262 A106607 A305082

Adjacent sequences: A033496 A033497 A033498 * A033500 A033501 A033502

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(41) onward added by G. C. Greubel, Oct 14 2019

Status

approved