A375279 Expansion of (1 - x - x^3)/((1 - x - x^3)^2 - 4*x^4).

1, 1, 1, 2, 7, 16, 30, 61, 137, 303, 644, 1365, 2936, 6340, 13625, 29209, 62701, 134758, 289547, 621816, 1335378, 2868341, 6161329, 13233947, 28424456, 61052489, 131135696, 281667368, 604991601, 1299458257, 2791106585, 5995020362, 12876698159, 27657838272

Offset: 0

Author

Seiichi Manyama, Aug 09 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A108479, A375278.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec((1-x-x^3)/((1-x-x^3)^2-4*x^4))

PARI

a(n) = sum(k=0, n\3, binomial(2*n-4*k, 2*k));

Formula

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-6).

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-4*k,2*k).