A320376 Number of parts in all partitions of n with largest multiplicity six.

6, 0, 7, 7, 15, 15, 38, 39, 67, 84, 131, 160, 242, 293, 421, 537, 730, 912, 1234, 1533, 2021, 2525, 3269, 4053, 5185, 6394, 8080, 9948, 12425, 15219, 18893, 23006, 28319, 34379, 42024, 50788, 61736, 74279, 89795, 107674, 129483, 154660, 185221, 220424, 262820

Offset

6,1

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Formula

a(n) ~ log(7) * exp(2*Pi*sqrt(n/7)) / (2 * Pi * 7^(1/4) * n^(1/4)). - Vaclav Kotesovec, Oct 25 2018

Maple

b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
    end:
a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(6):
seq(a(n), n=6..50);

Crossrefs

Column k=6 of A213177.

Sequence in context: A196915 A249651 A021626 * A059956 A245700 A201521

Adjacent sequences: A320373 A320374 A320375 * A320377 A320378 A320379

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2018

Status

approved