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

%I A104648 #13 Nov 18 2020 06:50:36
%S A104648 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 A104648 86,96,108,121,134,150,168,185,204,228,254,279,308,339,377,411,453,
%U A104648 496,541,597,653,713,782,851,928,1013,1105,1200,1299,1420,1540,1674,1812,1960
%N A104648 Cardinality of set of sets of parts of all partitions of n into odd parts.
%H A104648 Alois P. Heinz, <a href="/A104648/b104648.txt">Table of n, a(n) for n = 0..150</a>
%e A104648 a(7) = |{{1}, {7}, {1, 3}, {1, 5}}| = 4.
%p A104648 b:= proc(n, i) option remember; `if`(n=0, {{}}, `if`(i<1, {},
%p A104648       {b(n, i-2)[], `if`(i>n, [][], map(x-> {x[], i}, b(n-i, i))[])}))
%p A104648     end:
%p A104648 a:= n-> nops(b(n, n-1+irem(n, 2))):
%p A104648 seq(a(n), n=0..60);  # _Alois P. Heinz_, Jun 30 2016
%t A104648 a[n_] := Union /@ IntegerPartitions[n, All, Range[1, n, 2]] // Union // Length;
%t A104648 a /@ Range[0, 60] (* _Jean-François Alcover_, Nov 18 2020 *)
%Y A104648 Cf. A088314.
%K A104648 nonn
%O A104648 0,4
%A A104648 _Vladeta Jovovic_, Apr 21 2005
%E A104648 More terms from _David Wasserman_, Apr 24 2008
%E A104648 a(0)=1 from _Alois P. Heinz_, Jun 30 2016