A376791 Expansion of 1/sqrt((1 - x^3)^2 - 4*x).

1, 2, 6, 21, 76, 282, 1065, 4074, 15732, 61193, 239406, 941064, 3713701, 14703896, 58383138, 232383841, 926943678, 3704410890, 14828984641, 59450138412, 238659074286, 959247218253, 3859777477944, 15546444564846, 62675854384977, 252893414725842, 1021208266423260

Offset: 0

Author

Seiichi Manyama, Oct 04 2024

Keywords

• nonn

Comments

From Seiichi Manyama, Apr 30 2025: (Start)

Number of lattice paths from (0,0) to (n,n) using steps (1,0),(0,1),(3,3).

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

Crossrefs

Cf. A001850, A349713, A376792.

Cf. A053442, A098479.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-x^3)^2-4*x))

PARI

a(n) = sum(k=0, n\3, binomial(2*n-5*k, k)*binomial(2*n-6*k, n-3*k));

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k,k) * binomial(2*n-6*k,n-3*k).