A375282 Expansion of (1 - x - x^4)/((1 - x - x^4)^2 - 4*x^5).

1, 1, 1, 1, 2, 7, 16, 29, 47, 82, 162, 331, 650, 1220, 2262, 4261, 8175, 15747, 30121, 57210, 108521, 206456, 393865, 751675, 1432772, 2728076, 5193901, 9893596, 18853664, 35928972, 68454369, 130403085, 248413549, 473261209, 901681650, 1717923403, 3272944760

Offset: 0

Author

Seiichi Manyama, Aug 09 2024

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,2,2,0,0,-1).

Crossrefs

Cf. A375279.

Programs

Mathematica

CoefficientList[Series[(1-x-x^4)/((1-x-x^4)^2-4x^5),{x,0,40}],x] (* or *) LinearRecurrence[{2,-1,0,2,2,0,0,-1},{1,1,1,1,2,7,16,29},40] (* Harvey P. Dale, May 24 2025 *)

PARI

my(N=40, x='x+O('x^N)); Vec((1-x-x^4)/((1-x-x^4)^2-4*x^5))

PARI

a(n) = sum(k=0, n\4, binomial(2*n-6*k, 2*k));

Formula

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) + 2*a(n-5) - a(n-8).

a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-6*k,2*k).