A387769 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*k+1,2*n-6*k+1).

1, 0, 0, 6, 2, 0, 20, 40, 4, 56, 280, 168, 152, 1344, 2016, 928, 5296, 14784, 11392, 20064, 82400, 111744, 104000, 389376, 828096, 814720, 1758848, 5001856, 6719616, 9121792, 26429440, 48694272, 59535616, 133009408, 306595840, 430181888, 710558208, 1738592256

Offset

0,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,4,4,0,-4,8,-4).

Formula

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

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

Mathematica

Table[Sum[2^k*Binomial[2*k+1, 2*n-6*k+1], {k, 0, Floor[n/2]}], {n, 0, 35}] (* Vincenzo Librandi, Sep 13 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, 2^k*binomial(2*k+1, 2*n-6*k+1));
(Magma) [&+[2^k * Binomial(2*k+1, 2*n-6*k+1): k in [0..Floor(n/3)]]: n in [0..40]]; // Vincenzo Librandi, Sep 13 2025

Crossrefs

Cf. A387767, A387768.

Sequence in context: A021621 A197844 A326825 * A182639 A244135 A120002

Adjacent sequences: A387766 A387767 A387768 * A387770 A387771 A387772

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 07 2025

Status

approved