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

1,2

Links

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

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

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(2*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, 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 *)

Crossrefs

Column k=4 of A210485.

Cf. A035959.

Sequence in context: A290258 A277335 A267353 * A281063 A032602 A116593

Adjacent sequences: A320604 A320605 A320606 * A320608 A320609 A320610

Keyword

nonn

Author

Alois P. Heinz, Oct 17 2018

Status

approved