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

Author

Gus Wiseman, May 07 2019

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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}]

Extensions

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