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

%I #13 Nov 18 2020 06:50:36

%S 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,

%T 86,96,108,121,134,150,168,185,204,228,254,279,308,339,377,411,453,

%U 496,541,597,653,713,782,851,928,1013,1105,1200,1299,1420,1540,1674,1812,1960

%N Cardinality of set of sets of parts of all partitions of n into odd parts.

%H Alois P. Heinz, <a href="/A104648/b104648.txt">Table of n, a(n) for n = 0..150</a>

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

%p b:= proc(n, i) option remember; `if`(n=0, {{}}, `if`(i<1, {},

%p {b(n, i-2)[], `if`(i>n, [][], map(x-> {x[], i}, b(n-i, i))[])}))

%p end:

%p a:= n-> nops(b(n, n-1+irem(n, 2))):

%p seq(a(n), n=0..60); # _Alois P. Heinz_, Jun 30 2016

%t a[n_] := Union /@ IntegerPartitions[n, All, Range[1, n, 2]] // Union // Length;

%t a /@ Range[0, 60] (* _Jean-François Alcover_, Nov 18 2020 *)

%Y Cf. A088314.

%K nonn

%O 0,4

%A _Vladeta Jovovic_, Apr 21 2005

%E More terms from _David Wasserman_, Apr 24 2008

%E a(0)=1 from _Alois P. Heinz_, Jun 30 2016