A390702 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k+1,n-3*k).

1, 3, 10, 36, 132, 490, 1837, 6939, 26367, 100673, 385917, 1484327, 5725413, 22138911, 85790874, 333080508, 1295351352, 5045196654, 19676805486, 76835246652, 300363422658, 1175362836576, 4603607339604, 18046523089450, 70799319866224, 277958176566102, 1091998266879348

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = [x^n] 1/((1-x^3) * (1-x)^(n+2)).

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

Mathematica

Table[Sum[(-3)^k*Binomial[2*n+k+4, n-k], {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 18 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k+1, n-3*k));
(Magma) [&+[(-3)^k*Binomial(2*n+k+4, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 18 2025

Crossrefs

Cf. A001840, A390703, A390704.

Cf. A105872, A371758, A371871.

Sequence in context: A149040 A055989 A329533 * A102871 A371842 A277287

Adjacent sequences: A390699 A390700 A390701 * A390703 A390704 A390705

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved