A307040 a(n) = Sum_{k=0..floor(n/6)} (-1)^k*binomial(n,6*k).

1, 1, 1, 1, 1, 1, 0, -6, -27, -83, -209, -461, -922, -1702, -2911, -4549, -6187, -6187, 0, 23238, 87021, 238337, 564719, 1217483, 2434966, 4542526, 7865521, 12403951, 16942381, 16942381, 0, -63239286, -236031147, -644886923, -1525870529, -3287837741, -6575675482

Offset: 0

Author

Seiichi Manyama, Mar 21 2019

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-2).

Crossrefs

Column 6 of A307039.

Cf. A306847.

Programs

Mathematica

a[n_] := Sum[(-1)^k * Binomial[n,6*k], {k,0,Floor[n/6]}]; Array[a, 37, 0] (* Amiram Eldar, May 25 2021 *)

PARI

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

PARI

N=66; x='x+O('x^N); Vec((1-x)^5/((1-x)^6+x^6))

Formula

G.f.: (1 - x)^5/((1 - x)^6 + x^6).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - 2*a(n-6) for n > 5.