A104648 Cardinality of set of sets of parts of all partitions of n into odd parts.

1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 9, 11, 13, 15, 18, 20, 24, 28, 31, 36, 41, 47, 52, 60, 68, 76, 86, 96, 108, 121, 134, 150, 168, 185, 204, 228, 254, 279, 308, 339, 377, 411, 453, 496, 541, 597, 653, 713, 782, 851, 928, 1013, 1105, 1200, 1299, 1420, 1540, 1674, 1812, 1960

Offset: 0

Author

Vladeta Jovovic, Apr 21 2005

Keywords

• nonn

Examples

			a(7) = |{{1}, {7}, {1, 3}, {1, 5}}| = 4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A088314.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, {{}}, `if`(i<1, {},
      {b(n, i-2)[], `if`(i>n, [][], map(x-> {x[], i}, b(n-i, i))[])}))
    end:
a:= n-> nops(b(n, n-1+irem(n, 2))):
seq(a(n), n=0..60);  # Alois P. Heinz, Jun 30 2016

Mathematica

a[n_] := Union /@ IntegerPartitions[n, All, Range[1, n, 2]] // Union // Length;
a /@ Range[0, 60] (* Jean-François Alcover, Nov 18 2020 *)

Extensions

More terms from David Wasserman, Apr 24 2008

a(0)=1 from Alois P. Heinz, Jun 30 2016