A387483 a(n) = Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(k,n-2*k)^2.

1, 0, 2, 4, 4, 32, 24, 144, 304, 576, 2336, 3648, 13120, 30208, 70528, 218368, 456448, 1360896, 3316224, 8311808, 23127040, 54812672, 151197696, 380669952, 978595840, 2613067776, 6540566528, 17464705024, 44764708864, 116183662592, 305637064704, 783627386880

Offset

0,3

Links

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

Formula

G.f.: 1/sqrt((1-2*x^2-4*x^3)^2 - 32*x^5).

D-finite with recurrence n*a(n) +4*(-n+1)*a(n-2) +4*(-2*n+3)*a(n-3) +4*(n-2)*a(n-4) +8*(-2*n+5)*a(n-5) +16*(n-3)*a(n-6)=0. - R. J. Mathar, Sep 07 2025

Mathematica

Table[Sum[2^(n-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, 2^(n-k)*binomial(k, n-2*k)^2);
(Magma) [(&+[2^(n-k)* Binomial(k, n-2*k)^2: k in [0..Floor(n/2)]]): n in [0..40]]; // Vincenzo Librandi, Sep 01 2025

Crossrefs

Cf. A298567.

Sequence in context: A092524 A137787 A225171 * A320600 A360685 A290606

Adjacent sequences: A387480 A387481 A387482 * A387484 A387485 A387486

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2025

Status

approved