A392429 a(n) = Sum_{k=0..floor(2*n/5)} binomial(2*k,2*n-5*k).

1, 0, 0, 2, 0, 1, 6, 1, 6, 20, 7, 28, 70, 38, 121, 253, 186, 505, 938, 859, 2069, 3553, 3822, 8390, 13700, 16577, 33834, 53585, 70607, 136078, 211907, 296808, 546806, 844899, 1235681, 2197582, 3388668, 5107821, 8838423, 13647361, 21002403, 35582877, 55117511

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,1,-2,1).

Formula

G.f.: (1 - 2*x^3) / (1 - 4*x^3 - x^5*(1-x)^2).

a(n) = 4*a(n-3) + a(n-5) - 2*a(n-6) + a(n-7).

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-2*x^3)/(1-4*x^3-x^5*(1-x)^2))

Crossrefs

Cf. A391594, A108479, A392428, A376729, A376730, A392430, A376731.

Cf. A391265.

Sequence in context: A276436 A161121 A021500 * A383900 A175197 A376983

Adjacent sequences: A392426 A392427 A392428 * A392430 A392431 A392432

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 11 2026

Status

approved