A387679 Expansion of g/(1 + x^3*g^3), where g = 1+x*g^3 is the g.f. of A001764.

1, 1, 3, 11, 51, 255, 1341, 7304, 40857, 233353, 1355221, 7978929, 47514887, 285696430, 1732095126, 10576735463, 64991316063, 401570899119, 2493475888629, 15551029778099, 97371738375165, 611874791154832, 3857505029962595, 24391676516399403, 154653699978741121

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (3*k+1) * binomial(3*n-6*k+1,n-3*k)/(3*n-6*k+1).

Mathematica

Table[Sum[(-1)^k*(3*k+1)*Binomial[3*n-6*k+1, n-3*k]/(3*n-6*k+1), {k, 0, Floor[n/3]}], {n, 0, 30}] (* Vincenzo Librandi, Dec 02 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*(3*k+1)*binomial(3*n-6*k+1, n-3*k)/(3*n-6*k+1));
(Magma) [&+[(-1)^k*(3*k+1)*Binomial(3*n-6*k+1, n-3*k)/(3*n-6*k+1): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Dec 02 2025

Crossrefs

Cf. A387676, A387678, A390517.

Cf. A001764, A391062.

Sequence in context: A359146 A199212 A113283 * A326519 A127784 A112696

Adjacent sequences: A387676 A387677 A387678 * A387680 A387681 A387682

Keyword

nonn

Author

Seiichi Manyama, Nov 30 2025

Status

approved