A307158 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n,3*k)^2.

1, 1, 1, 0, -15, -99, -398, -1175, -2351, 0, 29601, 183195, 756978, 2351805, 4885791, 0, -63746991, -400000275, -1675991918, -5274560891, -11081420615, 0, 147257373891, 931226954949, 3929550225586, 12446852889901, 26304183607651, 0, -353181028924809

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1752

Formula

a(6*n+3) = 0 for n >= 0.

Mathematica

a[n_] := Sum[(-1)^k * Binomial[n, 3*k]^2, {k, 0, Floor[n/3]}]; Array[a, 30, 0] (* Amiram Eldar, May 20 2021 *)

Prog

(PARI) {a(n) = sum(k=0, n\3, (-1)^k*binomial(n, 3*k)^2)}

Crossrefs

Central coefficients of number triangle A307156.

Cf. A057681, A119363, A307091.

Sequence in context: A108254 A174383 A341396 * A000973 A034266 A087661

Adjacent sequences: A307155 A307156 A307157 * A307159 A307160 A307161

Keyword

sign

Author

Seiichi Manyama, Mar 27 2019

Status

approved