A387747 a(n) = (1/4) * Sum_{k=0..n-1} binomial(6*n,6*k+3).

0, 5, 110, 12563, 654764, 45934985, 2831026490, 184123634063, 11704588234904, 751235404352165, 48021238430944070, 3074920600665471563, 196752762233293800644, 12593315000581805484545, 805941428160658490440850, 51581081162949724023605063, 3301166790890757660355175984

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..250

Index entries for linear recurrences with constant coefficients, signature (38,1691,-1728).

Formula

G.f.: x * (5-80*x-72*x^2)/((1-64*x) * (1-x) * (1+27*x)).

a(n) = 38*a(n-1) + 1691*a(n-2) - 1728*a(n-3) for n > 3.

E.g.f.: (exp(64*x) + 2*exp(x) - 2*exp(-27*x) - 1)/24. - Stefano Spezia, Sep 07 2025

Mathematica

Table[(1/4)*Sum[Binomial[6*n, 6*k+3], {k, 0, n-1}], {n, 0, 18}] (* Vincenzo Librandi, Sep 09 2025 *)

Prog

(PARI) a(n) = sum(k=0, n-1, binomial(6*n, 6*k+3))/4;
(Magma) [&+[(1/4)* Binomial(6*n, 6*k+3): k in [0..n]]: n in [0..19]]; // Vincenzo Librandi, Sep 09 2025

Crossrefs

Cf. A070967, A387745, A387746.

Sequence in context: A203367 A322631 A294965 * A219161 A367248 A284461

Adjacent sequences: A387744 A387745 A387746 * A387748 A387749 A387750

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 06 2025

Status

approved