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A104648
Cardinality of set of sets of parts of all partitions of n into odd parts.
1
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
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
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