A392404 a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-5*k,3*k).

1, 1, 1, 1, 2, 11, 36, 85, 167, 315, 666, 1605, 3974, 9394, 21051, 46066, 101850, 230720, 530476, 1217951, 2769267, 6247570, 14077081, 31830492, 72252193, 164222206, 372849637, 845040005, 1913511381, 4333973765, 9823382586, 22277085184, 50520092158, 114537197118

Offset

0,5

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,2,6,0,0,-1).

Formula

G.f.: ((1-x)^2 - x^4 - x^5) / ((1-x)^3 - 2*x^4 - 6*x^5 + x^8).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 2*a(n-4) + 6*a(n-5) - a(n-8).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(((1-x)^2-x^4-x^5)/((1-x)^3-2*x^4-6*x^5+x^8))

Crossrefs

Cf. A387843, A392400, A392401, A392402, A392403, A392405.

Sequence in context: A078982 A154416 A184538 * A316322 A392402 A238706

Adjacent sequences: A392401 A392402 A392403 * A392405 A392406 A392407

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 10 2026

Status

approved