A320612 Number of parts in all partitions of n in which no part occurs more than nine times.

1, 3, 6, 12, 20, 35, 54, 86, 128, 182, 264, 376, 520, 718, 978, 1318, 1761, 2338, 3070, 4008, 5206, 6707, 8604, 10982, 13933, 17604, 22155, 27745, 34627, 43061, 53338, 65859, 81074, 99458, 121687, 148469, 180633, 219202, 265386, 320473, 386147, 464245, 556925

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=9 of A210485.

Cf. A261776.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(9*i*(i+1)/2 [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 9))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..50);

Mathematica

Table[Length[  Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 9 &]]], {n, 43}] (* Robert Price, Jul 31 2020 *)

Formula

a(n) ~ log(10) * exp(Pi*sqrt(3*n/5)) / (2 * Pi * 15^(1/4) * n^(1/4)). - Vaclav Kotesovec, Oct 18 2018