OFFSET
0,4
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).
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.
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 *)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(2*n-5*k, k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 12 2024
STATUS
approved