A390706 a(n) = Sum_{k=0..floor(n/3)} binomial(4*n-3*k-2,n-3*k).

1, 2, 15, 121, 1012, 8673, 75583, 666675, 5933931, 53190814, 479494265, 4342462644, 39478385801, 360077007227, 3293377459254, 30195048974487, 277425590666292, 2553674670598785, 23545217250972991, 217411251736357778, 2010198896418933729, 18608805727835754069

Offset

0,2

Links

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

Formula

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

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

Mathematica

Table[Sum[(-3)^k*Binomial[4*n +k+1, n-k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(4*n-3*k-2, n-3*k));
(Magma) [&+[(-3)^k*Binomial(4*n+k+1, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A371871, A390705.

Cf. A371771, A387990, A390704, A390708.

Sequence in context: A074621 A341929 A185758 * A052448 A168502 A369108

Adjacent sequences: A390703 A390704 A390705 * A390707 A390708 A390709

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved