A364595 G.f. satisfies A(x) = 1/(1-x) + x^3*(1-x)*A(x)^3.
1, 1, 1, 2, 3, 4, 8, 15, 25, 50, 102, 193, 390, 815, 1645, 3385, 7141, 14893, 31196, 66309, 140752, 299043, 640367, 1373929, 2950006, 6360976, 13749865, 29753891, 64547097, 140329453, 305470485, 666084272, 1454920255, 3181946080, 6968134645, 15280422274
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(n-2*k, k)*binomial(3*k, k)/(2*k+1));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(3*k,k) / (2*k+1).