A375308 a(n) = Sum_{k=0..floor(2*n/3)} binomial(4*n-4*k,2*k).

1, 1, 7, 30, 137, 644, 2936, 13625, 62701, 289547, 1335378, 6161329, 28424456, 131135696, 604991601, 2791106585, 12876698159, 59406240678, 274068969337, 1264408966284, 5833313285128, 26911817257385, 124156868897413, 572794023175795, 2642568194952474

Offset: 0

Author

Seiichi Manyama, Aug 11 2024

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (2,11,6,-6,4,-1).

Crossrefs

Cf. A108479, A375279, A375307, A375314.

Programs

PARI

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

PARI

my(N=30, x='x+O('x^N)); Vec((1-x-6*x^2-x^3)/((1-x+2*x^2-x^3)^2-16*x^2))

Formula

a(n) = A375279(2*n).

a(n) = A375314(2*n).

a(n) = 2*a(n-1) + 11*a(n-2) + 6*a(n-3) - 6*a(n-4) + 4*a(n-5) - a(n-6).

G.f.: (1 - x - 6*x^2 - x^3)/((1 - x + 2*x^2 - x^3)^2 - 16*x^2).