A051033 a(n) = binomial(n, floor(n/3)).

1, 1, 1, 3, 4, 5, 15, 21, 28, 84, 120, 165, 495, 715, 1001, 3003, 4368, 6188, 18564, 27132, 38760, 116280, 170544, 245157, 735471, 1081575, 1562275, 4686825, 6906900, 10015005, 30045015, 44352165, 64512240, 193536720, 286097760, 417225900, 1251677700, 1852482996

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ 3^(n+1) / (2^((2*n + (n mod 3))/3+1) * sqrt(Pi*n)). - Amiram Eldar, Sep 17 2025

Maple

[seq(binomial(n, floor(n/3)), n=0..50)];

Mathematica

a[n_] := Binomial[n, Floor[n/3]]; Array[a, 50, 0] (* Enrique Pérez Herrero, Mar 06 2012 *)

Prog

(PARI) a(n) = binomial(n, n\3); \\ Amiram Eldar, Sep 17 2025

Crossrefs

Cf. A001405, A051036, A051052, A051053, A062947.

Cf. A047193.

Sequence in context: A240670 A048040 A347391 * A346601 A242787 A031199

Adjacent sequences: A051030 A051031 A051032 * A051034 A051035 A051036

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved