A320611 Number of parts in all partitions of n in which no part occurs more than eight times.

1, 3, 6, 12, 20, 35, 54, 86, 119, 182, 254, 366, 499, 697, 934, 1274, 1681, 2237, 2918, 3830, 4927, 6377, 8128, 10388, 13120, 16600, 20796, 26076, 32419, 40318, 49798, 61494, 75464, 92582, 112990, 137800, 167284, 202912, 245128, 295870, 355813, 427472, 511926

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000

Formula

a(n) ~ log(3) * exp(4*Pi*sqrt(n/3)/3) / (Pi * sqrt(2) * 3^(1/4) * n^(1/4)). - Vaclav Kotesovec, Oct 18 2018

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(4*i*(i+1)<n, 0, add(
      (l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 8))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..50);

Mathematica

Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 8 &]]], {n, 43}] (* Robert Price, Jul 31 2020 *)

Crossrefs

Column k=8 of A210485.

Cf. A104502.

Sequence in context: A182978 A320609 A320610 * A320612 A320613 A006128

Adjacent sequences: A320608 A320609 A320610 * A320612 A320613 A320614

Keyword

nonn

Author

Alois P. Heinz, Oct 17 2018

Status

approved