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A371754
a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-2*k,n-3*k).
4
1, 3, 15, 85, 505, 3081, 19125, 120173, 761995, 4865697, 31244029, 201544551, 1305039209, 8477521051, 55221311565, 360559717807, 2359123470971, 15463951609491, 101530816122729, 667587477393509, 4395294402200983, 28972295880583861, 191181607835416543
OFFSET
0,2
FORMULA
a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(2*n)).
a(n) ~ 3^(3*n + 5/2) / (17 * sqrt(Pi*n) * 2^(2*n)). - Vaclav Kotesovec, Apr 05 2024
MATHEMATICA
Table[Sum[Binomial[3n-2k, n-3k], {k, 0, Floor[n/3]}], {n, 0, 30}] (* Harvey P. Dale, Oct 19 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(3*n-2*k, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 05 2024
STATUS
approved