A363338 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^(3*k)) * x^k/k ).
1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 1, 0, 2, 4, 2, 1, 5, 5, 1, 2, 4, 3, 2, 2, 2, 5, 5, 1, 4, 8, 4, 1, 5, 5, 2, 2, 2, 3, 4, 2, 1, 5, 5, 2, 3, 4, 2, 1, 3, 3, 2, 2, 5, 6, 3, 5, 8, 5, 2, 5, 6, 6, 6, 4, 9, 15, 9, 6, 17, 16, 5, 9
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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PARI
seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, x^(3*k))*x^k/k)+x*O(x^n))); Vec(A);
Formula
A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+x^(3*k+1))^a(k).
A(x) * A(w*x) * A(w^2*x) = A(x^3), where w = exp(2*Pi*i/3).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k and d==1 mod 3} (-1)^(k/d+1) * d * a(floor(d/3)) ) * a(n-k).