A383571 Expansion of 1/sqrt((1-x^3)^2 - 4*x^4).

1, 0, 0, 1, 2, 0, 1, 6, 6, 1, 12, 30, 21, 20, 90, 141, 100, 210, 561, 672, 672, 1681, 3206, 3528, 5125, 11622, 17892, 21253, 38172, 74052, 102565, 141680, 268092, 454741, 622182, 979836, 1790361, 2784366, 3993132, 6741593, 11587758, 17380116, 26551097, 45489082, 74098518

Offset: 0

Author

Seiichi Manyama, Apr 30 2025

Keywords

• nonn

Comments

Number of lattice paths from (0,0) to (n,n) using steps (4,0),(0,4),(3,3).

Diagonal of the rational function 1 / (1 - x^4 - y^4 - x^3*y^3).

Crossrefs

Cf. A053442, A376791.

Cf. A002426, A182883, A383572.

Programs

PARI

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

Formula

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