A321142 Number of strict integer partitions of 2*n with no subset summing to n.
0, 1, 2, 3, 5, 7, 11, 15, 23, 30, 43, 57, 79, 102, 138, 174, 232, 292, 375, 471, 602, 741, 935, 1148, 1425, 1733, 2137, 2571, 3156, 3789, 4557, 5470, 6582, 7796, 9317, 11027, 13058, 15400, 18159, 21249, 24971, 29170, 33986, 39596, 46073, 53219, 61711, 71330, 82171
Offset: 0
Keywords
Examples
The a(1) = 1 through a(8) = 23 partitions:
(2) (4) (6) (8) (10) (12) (14) (16)
(3,1) (4,2) (5,3) (6,4) (7,5) (8,6) (9,7)
(5,1) (6,2) (7,3) (8,4) (9,5) (10,6)
(7,1) (8,2) (9,3) (10,4) (11,5)
(5,2,1) (9,1) (10,2) (11,3) (12,4)
(6,3,1) (11,1) (12,2) (13,3)
(7,2,1) (5,4,3) (13,1) (14,2)
(7,3,2) (6,5,3) (15,1)
(7,4,1) (8,4,2) (7,5,4)
(8,3,1) (8,5,1) (7,6,3)
(9,2,1) (9,3,2) (9,4,3)
(9,4,1) (9,5,2)
(10,3,1) (9,6,1)
(11,2,1) (10,4,2)
(8,3,2,1) (10,5,1)
(11,3,2)
(11,4,1)
(12,3,1)
(13,2,1)
(6,5,4,1)
(7,4,3,2)
(9,4,2,1)
(10,3,2,1)
Links
- Fausto A. C. Cariboni, Table of n, a(n) for n = 0..200
Programs
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Mathematica
Table[Length[Select[IntegerPartitions[n],And[UnsameQ@@#,!Or@@Table[SameQ[Total[#[[s]]],n/2],{s,Subsets[Range[Length[#]]]}]]&]],{n,2,20,2}]
Extensions
a(33)-a(48) from Giovanni Resta, Oct 30 2018