A387482 a(n) = Sum_{k=0..floor(n/3)} 3^k * 2^(n-3*k) * binomial(k,n-3*k)^2.

1, 0, 0, 3, 6, 0, 9, 72, 36, 27, 486, 972, 297, 2592, 11664, 10611, 13446, 97200, 195129, 149688, 663876, 2334987, 2838726, 4697676, 21485817, 43705008, 51438240, 171480483, 517850982, 760446144, 1440329769, 5065354440, 10479570372, 15691149819, 44973017478

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Formula

G.f.: 1/sqrt((1-3*x^3-6*x^4)^2 - 72*x^7).

D-finite with recurrence -n*a(n) +3*(2*n-3)*a(n-3) +12*(n-2)*a(n-4) +9*(-n+3)*a(n-6) +18*(2*n-7)*a(n-7) +36*(-n+4)*a(n-8)=0. - R. J. Mathar, Sep 07 2025

Mathematica

Table[Sum[3^k* 2^(n-3*k)*Binomial[k, n-3*k]^2, {k, 0, Floor[n/3]}], {n, 0, 40}] (* Vincenzo Librandi, Aug 31 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, 3^k*2^(n-3*k)*binomial(k, n-3*k)^2);
(Magma) [(&+[3^k * 2^(n-3*k) * Binomial(k, n-3*k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // Vincenzo Librandi, Aug 31 2025

Crossrefs

Cf. A387480, A387481.

Sequence in context: A388319 A378800 A287845 * A070297 A284896 A299032

Adjacent sequences: A387479 A387480 A387481 * A387483 A387484 A387485

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2025

Status

approved