|
|
A359906
|
|
Number of integer partitions of n with integer mean and integer median.
|
|
13
|
|
|
1, 2, 2, 4, 2, 8, 2, 10, 9, 14, 2, 39, 2, 24, 51, 49, 2, 109, 2, 170, 144, 69, 2, 455, 194, 116, 381, 668, 2, 1378, 2, 985, 956, 316, 2043, 4328, 2, 511, 2293, 6656, 2, 8634, 2, 8062, 14671, 1280, 2, 26228, 8035, 15991, 11614, 25055, 2, 47201, 39810, 65092
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
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
|
|
|
EXAMPLE
|
The a(1) = 1 through a(9) = 9 partitions:
1 2 3 4 5 6 7 8 9
11 111 22 11111 33 1111111 44 333
31 42 53 432
1111 51 62 441
222 71 522
321 2222 531
411 3221 621
111111 3311 711
5111 111111111
11111111
|
|
MATHEMATICA
|
Table[Length[Select[IntegerPartitions[n], IntegerQ[Mean[#]]&&IntegerQ[Median[#]]&]], {n, 1, 30}]
|
|
CROSSREFS
|
These partitions are ranked by A360009.
A360005(n)/2 gives median of prime indices.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|