A368895 a(n) = Sum_{k=0..floor(n/3)} (-n)^k * binomial(n-2*k,k).

1, 1, 1, -2, -7, -14, 13, 113, 337, 19, -2579, -10867, -9911, 71852, 431229, 741181, -2178783, -20081708, -51012467, 58414532, 1061935641, 3651310699, 1841181, -62090909433, -279070619279, -250335322449, 3913178936941, 22877592319648, 38634162528361

Offset

0,4

Links

Table of n, a(n) for n=0..28.

Formula

a(n) = [x^n] 1/(1 - x + n*x^3).

Mathematica

Join[{1}, Table[Sum[(-n)^k Binomial[n-2k, k], {k, 0, Floor[n/3]}], {n, 30}]] (* Harvey P. Dale, Apr 18 2026 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (-n)^k*binomial(n-2*k, k));

Crossrefs

Cf. A368891, A368894.

Sequence in context: A102154 A102153 A332542 * A331703 A032537 A072120

Adjacent sequences: A368892 A368893 A368894 * A368896 A368897 A368898

Keyword

sign,easy

Author

Seiichi Manyama, Jan 09 2024

Status

approved