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

0,4

Links

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

Example

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

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 *)

Crossrefs

Cf. A088314.

Sequence in context: A342518 A029041 A112582 * A141271 A097793 A015742

Adjacent sequences: A104645 A104646 A104647 * A104649 A104650 A104651

Keyword

nonn

Author

Vladeta Jovovic, Apr 21 2005

Extensions

More terms from David Wasserman, Apr 24 2008

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

Status

approved