A363404 - OEIS

A363404

G.f. satisfies A(x) = exp( Sum_{k>=1} (A(x^k) + A(w*x^k) + A(w^2*x^k))/3 * x^k/k ), where w = exp(2*Pi*i/3).

1, 1, 1, 1, 2, 2, 2, 4, 5, 5, 10, 12, 13, 26, 34, 36, 73, 96, 104, 210, 288, 315, 638, 881, 974, 1975, 2777, 3089, 6276, 8895, 9970, 20272, 29000, 32668, 66508, 95703, 108347, 220771, 319483, 363141, 740615, 1076331, 1227826, 2505979, 3655912, 4183309, 8544123, 12504292, 14347462

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OFFSET

0,5

LINKS

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

FORMULA

A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(3*k+1))^a(3*k).

A(x) * A(w*x) * A(w^2*x) = A(x^3).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k and d==1 mod 3} d * a(d-1) ) * a(n-k).

PROG

(PARI) seq(n) = my(w=exp(2*Pi*I/3), A=1); for(i=1, n, A=exp(sum(k=1, i, sum(m=0, 2, subst(A, x, w^m*x^k))/3*x^k/k)+x*O(x^n))); apply(round, Vec(A));

CROSSREFS