A383523 a(n) = Sum_{k=0..floor(n/4)} binomial(n,k) * binomial(n-3*k,k).

1, 1, 1, 1, 5, 11, 19, 29, 69, 163, 341, 639, 1319, 2913, 6343, 13061, 27029, 57699, 124813, 265583, 560385, 1191233, 2557743, 5486007, 11713623, 25013061, 53632099, 115219909, 247312763, 530489403, 1139262389, 2450199453, 5271832533, 11341427571, 24407218989

Offset

0,5

Comments

Diagonal of the rational function 1 / ((1-x)*(1-y) - x*y^4).

Links

Table of n, a(n) for n=0..34.

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n, k)*binomial(n-3*k, k));

Crossrefs

Cf. A000984, A002426, A383522.

Sequence in context: A338566 A387514 A352795 * A368898 A326665 A100920

Adjacent sequences: A383520 A383521 A383522 * A383524 A383525 A383526

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2025

Status

approved