|
|
A364272
|
|
Number of strict integer partitions of n containing the sum of some subset of the parts. A variation of sum-full strict partitions.
|
|
78
|
|
|
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 3, 1, 4, 3, 8, 6, 11, 10, 17, 16, 26, 25, 39, 39, 54, 60, 82, 84, 116, 126, 160, 177, 222, 242, 302, 337, 402, 453, 542, 601, 722, 803, 936, 1057, 1234, 1373, 1601, 1793, 2056, 2312, 2658, 2950, 3395, 3789, 4281, 4814, 5452, 6048
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,11
|
|
COMMENTS
|
First differs from A316402 at a(16) = 11 due to (7,5,3,1).
|
|
LINKS
|
|
|
EXAMPLE
|
The a(6) = 1 through a(16) = 11 partitions (A=10):
(321) . (431) . (532) (5321) (642) (5431) (743) (6432) (853)
(541) (651) (6421) (752) (6531) (862)
(4321) (5421) (7321) (761) (7431) (871)
(6321) (5432) (7521) (6532)
(6431) (9321) (6541)
(6521) (54321) (7432)
(7421) (7621)
(8321) (8431)
(8521)
(A321)
(64321)
|
|
MATHEMATICA
|
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, Total/@Subsets[#, {2, Length[#]}]]!={}&]], {n, 0, 30}]
|
|
CROSSREFS
|
The linear combination-free version is A364350.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|