A320613 Number of parts in all partitions of n in which no part occurs more than ten times.

1, 3, 6, 12, 20, 35, 54, 86, 128, 192, 264, 387, 531, 741, 1001, 1366, 1809, 2425, 3170, 4172, 5398, 6997, 8948, 11482, 14547, 18451, 23193, 29157, 36355, 45347, 56150, 69509, 85565, 105216, 128732, 157393, 191545, 232870, 282033, 341164, 411251, 495197, 594369

Offset

1,2

Links

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

Formula

a(n) ~ 3^(1/4) * log(11) * exp(2*Pi*sqrt(5*n/33)) / (2 * Pi * 55^(1/4) * n^(1/4)). - Vaclav Kotesovec, Oct 18 2018

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(5*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, 10))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..50);

Mathematica

Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 10 &]]], {n, 43}] (* Robert Price, Jul 31 2020 *)

Crossrefs

Column k=10 of A210485.

Sequence in context: A320610 A320611 A320612 * A006128 A247661 A079983

Adjacent sequences: A320610 A320611 A320612 * A320614 A320615 A320616

Keyword

nonn

Author

Alois P. Heinz, Oct 17 2018

Status

approved