OFFSET
0,3
COMMENTS
Cardinality of set of multisets of multiplicities of parts of all partitions of n. - Vladeta Jovovic, May 25 2008
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..125
EXAMPLE
a(7) = 10: [1], [7], [1,1], [1,2], [1,3] [1,4], [1,5], [2,3], [1,1,1], [1,1,2].
MAPLE
b:= proc(n, i) option remember; `if`(n=0, {[]}, `if`(i<1, {},
{b(n, i-1)[], seq(map(x->sort([x[], j]),
b(n-i*j, i-1))[], j=1..n/i)}))
end:
a:= n-> nops(b(n, n)):
seq(a(n), n=0..50); # Alois P. Heinz, Feb 19 2013
MATHEMATICA
a[n_] := Sort /@ ((Length /@ Split[#])& /@ IntegerPartitions[n]) // Union // Length;
a /@ Range[0, 50] (* Jean-François Alcover, Oct 31 2020 *)
PROG
(Python)
from sympy.utilities.iterables import partitions
def A088887(n): return len({tuple(sorted(p.values())) for p in partitions(n)}) # Chai Wah Wu, Sep 10 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Nov 28 2003
EXTENSIONS
More terms from Vladeta Jovovic, May 25 2008
STATUS
approved