A376792 Expansion of 1/sqrt((1 - x^4)^2 - 4*x).

1, 2, 6, 20, 71, 258, 954, 3572, 13501, 51404, 196858, 757472, 2926097, 11341032, 44080770, 171755976, 670664951, 2623732322, 10281616176, 40350944112, 158573538071, 623930435834, 2457658576132, 9690467310480, 38244489565051, 151064227161784, 597165099484632

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),(4,4).

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

Crossrefs

Cf. A001850, A349713, A376791.

Cf. A098482.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\4, binomial(2*n-7*k, k)*binomial(2*n-8*k, n-4*k));

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-7*k,k) * binomial(2*n-8*k,n-4*k).