A325512 Number of distinct nonzero numbers of partitions of n counted by length.

1, 1, 1, 1, 2, 2, 3, 4, 5, 7, 7, 7, 10, 9, 10, 12, 14, 15, 16, 16, 18, 19, 19, 20, 22, 23, 23, 25, 26, 27, 27, 28, 30, 31, 31, 33, 34, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 56, 58, 60, 61, 62, 63, 64, 65, 65

Offset

0,5

Comments

Also the number of distinct nonzero entries in row n of A008284.

Links

Table of n, a(n) for n=0..68.

Example

Row n = 9 of A008284 is (1, 4, 7, 6, 5, 3, 2, 1, 1), which has union {1,2,3,4,5,6,7}, so a(9) = 7.

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,
      b(n, i-1)+expand(x*b(n-i, min(n-i, i))))
    end:
a:= n-> nops({coeffs(b(n$2))}):
seq(a(n), n=0..90);  # Alois P. Heinz, Feb 23 2024

Mathematica

Table[Length[Union[Table[Length[IntegerPartitions[n, {k}]], {k, n}]]], {n, 30}]

Crossrefs

Cf. A001221, A006128, A007870, A008284, A056239, A116608, A181819, A302247.

Sequence in context: A316078 A082543 A050322 * A211858 A349149 A029012

Adjacent sequences: A325509 A325510 A325511 * A325513 A325514 A325515

Keyword

nonn

Author

Gus Wiseman, May 07 2019

Extensions

a(0)=1 prepended by Alois P. Heinz, Feb 23 2024

Status

approved