A390545 a(n) = Sum_{k=0..n} (-1)^k * binomial(3*n+3*k+1,n-k).

1, 3, 12, 57, 305, 1759, 10604, 65616, 412583, 2621660, 16782273, 108025849, 698383407, 4531073261, 29484836431, 192352647208, 1257627870829, 8238394509195, 54059595896575, 355273144800926, 2337995130437627, 15404896401182595, 101615126104698982, 670964309689031403

Offset

0,2

Links

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

Formula

G.f.: g/((1-3*x*g^2) * (1+x*g^6)) where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[(-1)^k*Binomial[3*n+3*k+1, n-k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 10 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(3*n+3*k+1, n-k));
(Magma) [&+[(-1)^k*Binomial(3*n+3*k+1, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 10 2025

Crossrefs

Cf. A005809, A371785, A390541, A390542, A390543, A390544.

Cf. A001764, A390452.

Sequence in context: A291695 A117107 A159609 * A128326 A323631 A014333

Adjacent sequences: A390542 A390543 A390544 * A390546 A390547 A390548

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2025

Status

approved