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

0,18

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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).

Prog

(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);

Crossrefs

Cf. A004111, A318133, A363339.

Cf. A363336.

Sequence in context: A208134 A175560 A143240 * A290260 A304273 A153659

Adjacent sequences: A363335 A363336 A363337 * A363339 A363340 A363341

Keyword

nonn

Author

Seiichi Manyama, May 28 2023

Status

approved