|
%I #13 Jan 25 2022 04:20:59
%S 0,1,2,3,5,7,11,15,23,30,43,57,79,102,138,174,232,292,375,471,602,741,
%T 935,1148,1425,1733,2137,2571,3156,3789,4557,5470,6582,7796,9317,
%U 11027,13058,15400,18159,21249,24971,29170,33986,39596,46073,53219,61711,71330,82171
%N Number of strict integer partitions of 2*n with no subset summing to n.
%H Fausto A. C. Cariboni, <a href="/A321142/b321142.txt">Table of n, a(n) for n = 0..200</a>
%e The a(1) = 1 through a(8) = 23 partitions:
%e (2) (4) (6) (8) (10) (12) (14) (16)
%e (3,1) (4,2) (5,3) (6,4) (7,5) (8,6) (9,7)
%e (5,1) (6,2) (7,3) (8,4) (9,5) (10,6)
%e (7,1) (8,2) (9,3) (10,4) (11,5)
%e (5,2,1) (9,1) (10,2) (11,3) (12,4)
%e (6,3,1) (11,1) (12,2) (13,3)
%e (7,2,1) (5,4,3) (13,1) (14,2)
%e (7,3,2) (6,5,3) (15,1)
%e (7,4,1) (8,4,2) (7,5,4)
%e (8,3,1) (8,5,1) (7,6,3)
%e (9,2,1) (9,3,2) (9,4,3)
%e (9,4,1) (9,5,2)
%e (10,3,1) (9,6,1)
%e (11,2,1) (10,4,2)
%e (8,3,2,1) (10,5,1)
%e (11,3,2)
%e (11,4,1)
%e (12,3,1)
%e (13,2,1)
%e (6,5,4,1)
%e (7,4,3,2)
%e (9,4,2,1)
%e (10,3,2,1)
%t Table[Length[Select[IntegerPartitions[n],And[UnsameQ@@#,!Or@@Table[SameQ[Total[#[[s]]],n/2],{s,Subsets[Range[Length[#]]]}]]&]],{n,2,20,2}]
%Y Cf. A002219, A006827, A108917, A237258, A275972, A279791, A284640, A305551.
%K nonn
%O 0,3
%A _Gus Wiseman_, Oct 28 2018
%E a(33)-a(48) from _Giovanni Resta_, Oct 30 2018
|
