A387871 a(n) = Sum_{k=0..n} binomial(2*n+1,5*k).

1, 1, 2, 22, 127, 474, 1574, 6008, 25773, 107883, 427351, 1669801, 6643782, 26789257, 107746282, 430470899, 1717012749, 6863694378, 27481113638, 109996928003, 439924466026, 1759098789526, 7035859329512, 28146676447417, 112595619434887, 450374698997499

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..700

Index entries for linear recurrences with constant coefficients, signature (5,-10,20,15,4).

Formula

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

a(n) = 5*a(n-1) - 10*a(n-2) + 20*a(n-3) + 15*a(n-4) + 4*a(n-5) for n > 4.

Mathematica

Table[Sum[Binomial[2*n+1, 5*k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Sep 14 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(2*n+1, 5*k));
(Magma) [&+[Binomial(2*n+1, 5*k): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Sep 14 2025

Crossrefs

Cf. A387844.

Sequence in context: A292452 A292732 A206418 * A255866 A330900 A356341

Adjacent sequences: A387868 A387869 A387870 * A387872 A387873 A387874

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 10 2025

Status

approved