A307041 a(n) = Sum_{k=0..floor(n/7)} (-1)^k*binomial(n,7*k).

1, 1, 1, 1, 1, 1, 1, 0, -7, -35, -119, -329, -791, -1715, -3430, -6419, -11319, -18767, -28763, -38759, -38759, 0, 149205, 571781, 1613129, 3964051, 8934121, 18874261, 37748522, 71705865, 129080161, 218205281, 339081225, 459957169, 459957169, 0, -1749692735

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 (7,-21,35,-35,21,-7).

Crossrefs

Column 7 of A307039.

Cf. A306852.

Programs

Mathematica

a[n_] := Sum[(-1)^k * Binomial[n,7*k], {k,0,Floor[n/7]}]; Array[a, 37, 0] (* Amiram Eldar, May 25 2021 *)

PARI

{a(n) = sum(k=0, n\7, (-1)^k*binomial(n, 7*k))}

PARI

N=66; x='x+O('x^N); Vec((1-x)^6/((1-x)^7+x^7))

Formula

G.f.: (1 - x)^6/((1 - x)^7 + x^7).

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) for n > 6.