OFFSET
1,11
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).
EXAMPLE
Triangle begins:
1
0 1
1 0 1
1 0 0 1
2 1 0 0 1
2 2 0 0 0 1
4 2 1 0 0 0 1
4 3 2 0 0 0 0 1
7 4 3 1 0 0 0 0 1
8 6 3 2 0 0 0 0 0 1
12 8 4 3 1 0 0 0 0 0 1
14 11 5 4 2 0 0 0 0 0 0 1
21 14 8 4 3 1 0 0 0 0 0 0 1
24 20 10 5 4 2 0 0 0 0 0 0 0 1
34 25 15 6 5 3 1 0 0 0 0 0 0 0 1
For example, row n = 9 counts the following partitions:
(7,1,1) (5,2,2) (3,3,3) (4,4,1) . . . . (9)
(3,3,1,1,1) (6,2,1) (4,3,2)
(4,2,1,1,1) (2,2,2,2,1) (5,3,1)
(5,1,1,1,1) (3,2,2,1,1)
(2,2,1,1,1,1,1)
(3,1,1,1,1,1,1)
(1,1,1,1,1,1,1,1,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], OddQ[Length[#]]&&Median[#]==k&]], {n, 15}, {k, n}]
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Jan 21 2023
STATUS
approved