|
| |
|
|
A361848
|
|
Number of integer partitions of n such that (maximum) <= 2*(median).
|
|
18
|
|
|
|
1, 2, 3, 5, 6, 9, 12, 15, 19, 26, 31, 40, 49, 61, 75, 93, 112, 137, 165, 199, 238, 289, 341, 408, 482, 571, 674, 796, 932, 1096, 1280, 1495, 1738, 2026, 2347, 2724, 3148, 3639, 4191, 4831, 5545, 6372, 7298, 8358, 9552, 10915, 12439, 14176, 16121, 18325
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
The a(1) = 1 through a(7) = 12 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(111) (31) (41) (42) (52)
(211) (221) (51) (61)
(1111) (2111) (222) (322)
(11111) (321) (331)
(2211) (421)
(21111) (2221)
(111111) (3211)
(22111)
(211111)
(1111111)
For example, the partition y = (3,2,2) has maximum 3 and median 2, and 3 <= 2*2, so y is counted under a(7).
|
|
|
MATHEMATICA
|
Table[Length[Select[IntegerPartitions[n], Max@@#<=2*Median[#]&]], {n, 30}]
|
|
|
CROSSREFS
|
For length instead of median we have A237755.
For minimum instead of median we have A237824.
For mean instead of median we have A361851.
A000975 counts subsets with integer median.
Cf. A008284, A013580, A027193, A061395, A067538, A111907, A240219, A324562, A359907, A361394, A361860.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
