A320607 Number of parts in all partitions of n in which no part occurs more than four times.

1, 3, 6, 12, 15, 29, 41, 65, 91, 132, 179, 257, 339, 465, 616, 823, 1062, 1402, 1790, 2320, 2939, 3750, 4701, 5946, 7398, 9243, 11428, 14161, 17368, 21372, 26056, 31823, 38596, 46838, 56499, 68208, 81868, 98292, 117489, 140390, 167068, 198796, 235655, 279239

Offset: 1

Author

Alois P. Heinz, Oct 17 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=4 of A210485.

Cf. A035959.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(2*i*(i+1) [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 4))))
    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,50}] (* Harvey P. Dale, May 18 2020 *)

Formula

a(n) ~ 3^(1/4) * log(5) * exp(2*Pi*sqrt(2*n/15)) / (2^(5/4) * 5^(1/4) * Pi * n^(1/4)). - Vaclav Kotesovec, Oct 18 2018