A387481 a(n) = Sum_{k=0..floor(n/2)} 3^k * 2^(n-2*k) * binomial(k,n-2*k)^2.

1, 0, 3, 6, 9, 72, 63, 486, 1053, 2808, 11907, 22518, 99225, 246888, 755487, 2554902, 6488829, 23112216, 63506835, 198653958, 623336553, 1781565192, 5807475711, 16898655942, 52699192029, 161995971384, 484990399395, 1525112887446, 4572778238649, 14184781485480, 43472894580063

Offset

0,3

Links

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

Formula

G.f.: 1/sqrt((1-3*x^2-6*x^3)^2 - 72*x^5).

D-finite with recurrence n*a(n) +6*(-n+1)*a(n-2) +6*(-2*n+3)*a(n-3) +9*(n-2)*a(n-4) +18*(-2*n+5)*a(n-5) +36*(n-3)*a(n-6)=0. - R. J. Mathar, Sep 07 2025

Mathematica

Table[Sum[3^k * 2^(n-2*k)*Binomial[k, n-2*k]^2, {k, 0, Floor[n/2]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 01 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, 3^k*2^(n-2*k)*binomial(k, n-2*k)^2);
(Magma) [(&+[3^k * 2^(n-2*k)* Binomial(k, n-2*k)^2: k in [0..Floor(n/2)]]): n in [0..40]]; // Vincenzo Librandi, Sep 01 2025

Crossrefs

Cf. A387480, A387482.

Sequence in context: A133195 A196156 A103978 * A289064 A293537 A073910

Adjacent sequences: A387478 A387479 A387480 * A387482 A387483 A387484

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2025

Status

approved