A383528 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(n-2*k,k).

1, 1, 1, 5, 11, 19, 57, 149, 325, 841, 2223, 5387, 13599, 35435, 89561, 227397, 587861, 1508833, 3865285, 9980185, 25767813, 66439737, 171835439, 445009955, 1152176511, 2986869731, 7752069847, 20125928723, 52286212535, 135949102339, 353648726393, 920409996709

Offset

0,4

Comments

Diagonal of the rational function 1 / ((1-x)*(1-y) - y^3).

Links

Table of n, a(n) for n=0..31.

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(n-2*k, k));

Crossrefs

Cf. A001850, A383529.

Sequence in context: A072743 A045452 A152085 * A394801 A386131 A386134

Adjacent sequences: A383525 A383526 A383527 * A383529 A383530 A383531

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2025

Status

approved