A306941 Expansion of 1/((1 - x)^8 + x^8).

1, 8, 36, 120, 330, 792, 1716, 3432, 6434, 11424, 19312, 31008, 46512, 62016, 62016, 0, -245156, -961376, -2787760, -7065760, -16478280, -36159840, -75522960, -151045920, -290021896, -534308096, -940325760, -1564496128, -2406819200, -3249142272, -3249142272

Offset: 0

Author

Seiichi Manyama, Mar 17 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 A306914.

Programs

Mathematica

CoefficientList[Series[1/((1 - x)^8 + x^8), {x, 0, 30}], x] (* Amiram Eldar, May 25 2021 *)

PARI

{a(n) = sum(k=0, n\8, (-1)^k*binomial(n+7, 8*k+7))}

PARI

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

Formula

a(n) = Sum_{k=0..floor(n/8)} (-1)^k*binomial(n+7,8*k+7).

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.