A391302 Expansion of g^2/(1 + x^3*g^4), where g = 1+x*g^3 is the g.f. of A001764.

1, 2, 7, 29, 137, 695, 3695, 20308, 114436, 657550, 3837986, 22692014, 135619965, 817991662, 4972692185, 30437169640, 187422668362, 1160229062798, 7216344400527, 45074402993754, 282618594386957, 1778172298429813, 11223145772872875, 71040444598820668

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (4*k+2) * binomial(3*n-5*k+2,n-3*k)/(3*n-5*k+2).

Mathematica

Table[ Sum[(-1)^k*(4*k+2)*Binomial[3*n-5*k+2, n-3*k]/(3*n-5*k+2), {k, 0, Floor[n/3]}], {n, 0, 21}] (* Vincenzo Librandi, Dec 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*(4*k+2)*binomial(3*n-5*k+2, n-3*k)/(3*n-5*k+2));
(Magma) [&+[(-1)^k*(4*k+2)*Binomial(3*n-5*k+2, n-3*k)/(3*n-5*k+2): k in [0..Floor(n/3)]] : n in [0..30] ]; // Vincenzo Librandi, Dec 07 2025

Crossrefs

Cf. A391296, A391298, A391300.

Cf. A001764, A391130.

Sequence in context: A183608 A307389 A104252 * A373802 A391300 A018977

Adjacent sequences: A391299 A391300 A391301 * A391303 A391304 A391305

Keyword

nonn

Author

Seiichi Manyama, Dec 06 2025

Status

approved