A390705 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-3*k-2,n-3*k).

1, 1, 6, 36, 217, 1332, 8295, 52221, 331518, 2118558, 13611144, 87833781, 568893156, 3696245515, 24080248485, 157245263196, 1028928699129, 6744977287656, 44287036450035, 291206172153066, 1917300157617312, 12638390384014515, 83398707478813197, 550874308524107364

Offset

0,3

Links

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

Formula

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

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

Mathematica

Table[Sum[(-3)^k*Binomial[3*n +k+1, n-k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 18 2025 *)

Prog

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

Crossrefs

Cf. A371871, A390706.

Sequence in context: A196869 A172489 A033142 * A082309 A004319 A129324

Adjacent sequences: A390702 A390703 A390704 * A390706 A390707 A390708

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved