A363239 Number of partitions of n with rank a multiple of 7.

1, 0, 1, 1, 1, 1, 3, 4, 4, 6, 8, 11, 15, 19, 26, 33, 43, 55, 70, 89, 114, 144, 179, 225, 280, 348, 430, 532, 653, 800, 978, 1193, 1449, 1758, 2127, 2569, 3091, 3717, 4455, 5334, 6369, 7596, 9039, 10739, 12734, 15080, 17822, 21039, 24791, 29176, 34277, 40227, 47133, 55165, 64468

Offset

1,7

Links

Table of n, a(n) for n=1..55.

Formula

G.f.: (1/Product_{k>=1} (1-x^k)) * Sum_{k>=1} (-1)^(k-1) * x^(k*(3*k-1)/2) * (1-x^k) * (1+x^(7*k)) / (1-x^(7*k)).

Maple

b:= proc(n, i, c) option remember; `if`(i>n, 0, `if`(i=n,
     `if`(irem(i-c, 7)=0, 1, 0), b(n-i, i, c+1)+b(n, i+1, c)))
    end:
a:= n-> b(n, 1$2):
seq(a(n), n=1..55);  # Alois P. Heinz, May 23 2023

Prog

(PARI) my(N=60, x='x+O('x^N)); Vec(1/prod(k=1, N, 1-x^k)*sum(k=1, N, (-1)^(k-1)*x^(k*(3*k-1)/2)*(1-x^k)*(1+x^(7*k))/(1-x^(7*k))))

Crossrefs

Cf. A000041, A328988, A340601, A363233, A363237, A363238.

Sequence in context: A224212 A078490 A282847 * A047877 A351371 A280448

Adjacent sequences: A363236 A363237 A363238 * A363240 A363241 A363242

Keyword

nonn

Author

Seiichi Manyama, May 23 2023

Status

approved