A307044 a(n) = Sum_{k=0..floor(n/8)} (-1)^k*binomial(n,8*k).

1, 1, 1, 1, 1, 1, 1, 1, 0, -8, -44, -164, -494, -1286, -3002, -6434, -12868, -24292, -43604, -74612, -121124, -183140, -245156, -245156, 0, 961376, 3749136, 10814896, 27293176, 63453016, 138975976, 290021896, 580043792, 1114351888, 2054677648, 3619173776

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 (8,-28,56,-70,56,-28,8,-2).

Crossrefs

Column 8 of A307039.

Cf. A306859.

Programs

Mathematica

a[n_] := Sum[(-1)^k * Binomial[n,8*k], {k,0,Floor[n/8]}]; Array[a, 36, 0] (* Amiram Eldar, May 25 2021 *)

PARI

{a(n) = sum(k=0, n\8, (-1)^k*binomial(n, 8*k))}

PARI

N=66; x='x+O('x^N); Vec((1-x)^7/((1-x)^8+x^8))

Formula

G.f.: (1 - x)^7/((1 - x)^8 + x^8).

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - 2*a(n-8) for n > 7.