A390704 a(n) = Sum_{k=0..floor(n/3)} binomial(4*n-3*k+1,n-3*k).

1, 5, 36, 287, 2394, 20502, 178641, 1575753, 14027013, 125753020, 1133772056, 10269202482, 93371557501, 851728271931, 7791006025224, 71438161410855, 656417278751730, 6042752353013481, 55719188030653477, 514534317709482548, 4757724412521071265, 44045808348497386536, 408209192573431778082

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+2)).

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

Mathematica

Table[Sum[(-3)^k*Binomial[4*n +k+4, 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+1, n-3*k));
(Magma) [&+[(-3)^k*Binomial(4*n+k+4, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A001840, A390702, A390703.

Cf. A371771, A387990, A390706, A390708.

Sequence in context: A253470 A188899 A052203 * A371775 A332624 A027331

Adjacent sequences: A390701 A390702 A390703 * A390705 A390706 A390707

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved