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

0,10

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).

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).

Mathematica

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

Prog

(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))

Crossrefs

Cf. A348308, A348310.

Cf. A099586, A348289.

Sequence in context: A366086 A099586 A253001 * A063258 A178964 A362342

Adjacent sequences: A348306 A348307 A348308 * A348310 A348311 A348312

Keyword

sign,easy

Author

Seiichi Manyama, Oct 11 2021

Status

approved