A348308 a(n) = Sum_{k=0..floor(n/6)} (-1)^k * binomial(n-3*k,3*k).

1, 1, 1, 1, 1, 1, 0, -3, -9, -19, -34, -55, -82, -112, -136, -135, -75, 99, 469, 1147, 2269, 3970, 6325, 9235, 12231, 14166, 12771, 4076, -18244, -63424, -143695, -273223, -464779, -722439, -1027959, -1317915, -1448612, -1146827, 52219, 2870965, 8337370, 17769349, 32615514, 54022692, 81938664

Offset: 0

Author

Seiichi Manyama, Oct 11 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,-1).

Crossrefs

Cf. A348309, A348310.

Cf. A057681, A100134.

Programs

Mathematica

LinearRecurrence[{3, -3, 1, 0, 0, -1}, {1, 1, 1, 1, 1, 1}, 45] (* Amiram Eldar, Oct 11 2021 *)

PARI

a(n) = sum(k=0, n\6, (-1)^k*binomial(n-3*k, 3*k));

PARI

my(N=66, x='x+O('x^N)); Vec((1-x)^2/((1-x)^3+x^6))

Formula

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

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