A373639 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k,k).

1, 1, 1, 2, 4, 6, 9, 16, 27, 43, 71, 119, 196, 322, 533, 882, 1455, 2402, 3970, 6558, 10829, 17887, 29548, 48804, 80608, 133146, 219925, 363254, 599998, 991044, 1636944, 2703794, 4465957, 7376591, 12184181, 20125051, 33241289, 54905857, 90690002, 149795989

Offset: 0

Author

Seiichi Manyama, Jun 12 2024

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,2,0,0,-1).

Crossrefs

Cf. A000930, A373640.

Cf. A052535, A122367, A373644.

Programs

Mathematica

LinearRecurrence[{1,0,2,0,0,-1},{1, 1, 1, 2, 4, 6},40] (* James C. McMahon, Jun 14 2024 *)
Table[Sum[Binomial[2n-5k,k],{k,0,Floor[n/3]}],{n,0,40}] (* Harvey P. Dale, Sep 29 2024 *)

PARI

a(n) = sum(k=0, n\3, binomial(2*n-5*k, k));

Formula

G.f.: 1 / (1 - x^3 - x/(1 - x^3)).

a(n) = a(n-1) + 2*a(n-3) - a(n-6) for n > 5.