OFFSET
0,8
COMMENTS
Extending the terminology of A124943, the "low mean" of a multiset is its mean rounded down.
EXAMPLE
Triangle begins:
1
0 1
0 1 1
0 2 0 1
0 2 2 0 1
0 4 2 0 0 1
0 4 3 3 0 0 1
0 7 4 3 0 0 0 1
0 7 10 0 4 0 0 0 1
0 12 6 7 4 0 0 0 0 1
0 12 16 8 0 5 0 0 0 0 1
0 19 21 10 0 5 0 0 0 0 0 1
0 19 24 15 12 0 6 0 0 0 0 0 1
0 30 32 18 14 0 6 0 0 0 0 0 0 1
0 30 58 23 16 0 0 7 0 0 0 0 0 0 1
0 45 47 57 0 19 0 7 0 0 0 0 0 0 0 1
Row k = 8 counts the following partitions:
. (41111) (611) . (71) . . . (8)
(32111) (521) (62)
(311111) (5111) (53)
(22211) (431) (44)
(221111) (422)
(2111111) (4211)
(11111111) (332)
(3311)
(3221)
(2222)
MATHEMATICA
meandown[y_]:=If[Length[y]==0, 0, Floor[Mean[y]]];
Table[Length[Select[IntegerPartitions[n], meandown[#]==k&]], {n, 0, 15}, {k, 0, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Jun 30 2023
STATUS
approved