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A373639
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k,k).
4
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
0,4
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