A383584 a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k-1,k) * binomial(k,n-4*k).

1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 0, 3, 12, 10, 0, 4, 30, 60, 35, 5, 60, 210, 280, 132, 105, 560, 1260, 1267, 630, 1260, 4200, 6938, 5796, 4236, 11550, 27729, 36396, 28644, 34155, 90100, 168663, 188100, 163020, 276573, 631290, 973830, 995280, 1068222, 2111252, 4104100

Offset

0,10

Links

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

Formula

G.f.: (1/2) * ( 1 + 1/sqrt(1 - 4*x^5/(1-x^4)^2) ).

Mathematica

Table[Sum[Binomial[n-3*k-1, k]* Binomial[k, n-4*k], {k, 0, Floor[n/4]}], {n, 0, 40}] (* Vincenzo Librandi, May 02 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n-3*k-1, k)*binomial(k, n-4*k));
(Magma) [&+[Binomial(n-3*k-1, k) * Binomial(k, n-4*k): k in [0..Floor(n div 4)]]: n in [0..45]]; // Vincenzo Librandi, May 02 2025

Crossrefs

Cf. A005717, A383583.

Cf. A383572.

Sequence in context: A011023 A284610 A388442 * A234017 A182057 A260928

Adjacent sequences: A383581 A383582 A383583 * A383585 A383586 A383587

Keyword

nonn

Author

Seiichi Manyama, May 01 2025

Status

approved