OFFSET
0,13
COMMENTS
Extending the terminology of A124944, the "high mean" of a multiset is obtained by taking the mean and rounding up.
EXAMPLE
Triangle begins:
1
0 1
0 1 1
0 1 1 1
0 1 3 0 1
0 1 3 2 0 1
0 1 6 3 0 0 1
0 1 6 4 3 0 0 1
0 1 11 5 4 0 0 0 1
0 1 11 13 0 4 0 0 0 1
0 1 18 9 8 5 0 0 0 0 1
0 1 18 21 10 0 5 0 0 0 0 1
0 1 29 28 12 0 6 0 0 0 0 0 1
0 1 29 32 18 14 0 6 0 0 0 0 0 1
0 1 44 43 23 16 0 7 0 0 0 0 0 0 1
0 1 44 77 27 19 0 0 7 0 0 0 0 0 0 1
Row n = 7 counts the following partitions:
. (1111111) (4111) (511) (61) . . (7)
(3211) (421) (52)
(31111) (331) (43)
(2221) (322)
(22111)
(211111)
MATHEMATICA
meanup[y_]:=If[Length[y]==0, 0, Ceiling[Mean[y]]];
Table[Length[Select[IntegerPartitions[n], meanup[#]==k&]], {n, 0, 15}, {k, 0, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Jun 30 2023
STATUS
approved