A371754 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-2*k,n-3*k).
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
Keywords
Programs
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Mathematica
Table[Sum[Binomial[3n-2k,n-3k],{k,0,Floor[n/3]}],{n,0,30}] (* Harvey P. Dale, Oct 19 2024 *) -
PARI
a(n) = sum(k=0, n\3, binomial(3*n-2*k, n-3*k));
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