A375314 a(n) = Sum_{k=0..floor(n/2)} binomial(4*k,n-2*k).

1, 0, 1, 4, 7, 12, 30, 68, 137, 292, 644, 1380, 2936, 6324, 13625, 29216, 62701, 134784, 289547, 621708, 1335378, 2868620, 6161329, 13233352, 28424456, 61053608, 131135696, 281665480, 604991601, 1299461088, 2791106585, 5995016764, 12876698159, 27657841516

Offset

0,4

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (0,1,4,6,4,1).

Formula

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

G.f.: 1/(1 - x^2*(1 + x)^4).

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(4*k, n-2*k));
(PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^2*(1+x)^4))

Crossrefs

Cf. A116090.

Sequence in context: A215329 A208724 A183336 * A102953 A111157 A255340

Adjacent sequences: A375311 A375312 A375313 * A375315 A375316 A375317

Keyword

nonn,easy

Author

Seiichi Manyama, Aug 11 2024

Status

approved