A348309 a(n) = Sum_{k=0..floor(n/8)} (-1)^k * binomial(n-4*k,4*k).

1, 1, 1, 1, 1, 1, 1, 1, 0, -4, -14, -34, -69, -125, -209, -329, -493, -705, -955, -1199, -1324, -1092, -56, 2560, 8025, 18313, 36353, 66273, 113525, 184653, 286257, 422377, 589028, 763912, 888378, 837502, 372835, -928725, -3776537, -9302337, -19226889, -36034869, -63099331, -104630831, -165212760

Offset: 0

Author

Seiichi Manyama, Oct 11 2021

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,0,0,0,-1).

Crossrefs

Cf. A348308, A348310.

Cf. A099586, A348289.

Programs

Mathematica

LinearRecurrence[{4, -6, 4, -1, 0, 0, 0, -1}, {1, 1, 1, 1, 1, 1, 1, 1}, 45] (* Amiram Eldar, Oct 11 2021 *)

PARI

a(n) = sum(k=0, n\8, (-1)^k*binomial(n-4*k, 4*k));

PARI

my(N=66, x='x+O('x^N)); Vec((1-x)^3/((1-x)^4+x^8))

Formula

G.f.: (1-x)^3/((1-x)^4 + x^8).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) - a(n-8).