A363336 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^(3*k)) * x^k/k ).

1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 7, 9, 11, 12, 15, 18, 20, 23, 29, 33, 38, 45, 52, 60, 72, 82, 94, 111, 128, 144, 170, 196, 222, 257, 297, 335, 388, 447, 506, 580, 668, 754, 863, 990, 1119, 1273, 1460, 1647, 1871, 2138, 2417, 2733, 3118, 3517, 3975, 4522, 5102, 5747, 6529, 7361

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(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} 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, subst(A, x, x^(3*k))*x^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A000081, A115593, A363337.

Cf. A363338.

Sequence in context: A173911 A076269 A143644 * A104410 A018048 A077564

Adjacent sequences: A363333 A363334 A363335 * A363337 A363338 A363339

Keyword

nonn

Author

Seiichi Manyama, May 28 2023

Status

approved