A390570 a(n) = Sum_{k=0..n} (-1)^k * binomial(3*n+k,n-k).

1, 2, 9, 49, 286, 1728, 10660, 66691, 421497, 2684605, 17203264, 110784699, 716332655, 4647649736, 30242407617, 197283062901, 1289773693278, 8448367214664, 55433528789674, 364278091220380, 2397104129388816, 15793429731476831, 104172265254890825, 687813757141884309

Offset

0,2

Links

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

Formula

G.f.: 1/((1-3*x*g^2) * (1+x*g^4)) where g = 1+x*g^3 is the g.f. of A001764.

a(n) = Sum_{k=0..n} binomial(n+2*k-2,k).

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

Mathematica

Table[Sum[(-1)^k*Binomial[3*n+k, n-k], {k, 0, n}], {n, 0, 22}] (* Vincenzo Librandi, Nov 11 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(3*n+k, n-k));
(Magma) [&+[(-1)^k*Binomial(3*n+k, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 11 2025

Crossrefs

Cf. A279561, A390571, A390572.

Cf. A371785, A388043.

Cf. A001764.

Sequence in context: A224140 A360103 A382454 * A389435 A370345 A000167

Adjacent sequences: A390567 A390568 A390569 * A390571 A390572 A390573

Keyword

nonn

Author

Seiichi Manyama, Nov 10 2025

Status

approved