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

1,2

Links

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

Formula

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

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(9*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, 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 *)

Crossrefs

Column k=9 of A210485.

Cf. A261776.

Sequence in context: A320609 A320610 A320611 * A320613 A006128 A247661

Adjacent sequences: A320609 A320610 A320611 * A320613 A320614 A320615

Keyword

nonn

Author

Alois P. Heinz, Oct 17 2018

Status

approved