A387555 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^(n-k) * binomial(2*k+2,2*n-6*k+1).

1, 0, 0, 8, 16, 0, 48, 320, 192, 256, 3584, 7168, 3328, 30720, 129024, 129024, 245760, 1622016, 3272704, 3293184, 16596992, 56360960, 74776576, 166985728, 752156672, 1552941056, 2268069888, 8638693376, 25806503936, 41498443776, 99265544192, 357275009024

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1500

Index entries for linear recurrences with constant coefficients, signature (0,0,8,16,0,-16,64,-64).

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A387484.

G.f.: 1/((1-4*x^3-8*x^4)^2 - 128*x^7).

a(n) = 8*a(n-3) + 16*a(n-4) - 16*a(n-6) + 64*a(n-7) - 64*a(n-8).

Mathematica

Table[Sum[2^(n-k)*Binomial[2*k+2, 2*n-6*k+1]/2, {k, 0, Floor[n/3]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 02 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, 2^(n-k)*binomial(2*k+2, 2*n-6*k+1))/2;
(Magma) [&+[2^(n-k) * Binomial(2*k+2, 2*n-6*k+1)/2: k in [0..Floor(n/3)]]: n in [0..40]]; // Vincenzo Librandi, Sep 02 2025

Crossrefs

Cf. A387484.

Sequence in context: A131446 A061746 A028585 * A073926 A396608 A392530

Adjacent sequences: A387552 A387553 A387554 * A387556 A387557 A387558

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 02 2025

Status

approved