A320608 Number of parts in all partitions of n in which no part occurs more than five times.

1, 3, 6, 12, 20, 29, 47, 71, 104, 150, 213, 292, 405, 547, 736, 977, 1292, 1688, 2198, 2834, 3638, 4636, 5890, 7431, 9347, 11684, 14564, 18067, 22348, 27531, 33813, 41378, 50504, 61438, 74561, 90208, 108896, 131096, 157485, 188717, 225682, 269285, 320691

Offset

1,2

Links

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

Formula

a(n) ~ log(6) * exp(Pi*sqrt(5*n)/3) / (2 * Pi * 5^(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)/2<n, 0, add(
      (l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 5))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..50);

Mathematica

Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 5 &]]], {n, 43}] (* Robert Price, Jul 31 2020 *)

Crossrefs

Column k=5 of A210485.

Cf. A219601.

Sequence in context: A308722 A320192 A160732 * A246147 A066140 A200067

Adjacent sequences: A320605 A320606 A320607 * A320609 A320610 A320611

Keyword

nonn

Author

Alois P. Heinz, Oct 17 2018

Status

approved