OFFSET
0,3
COMMENTS
Number of integer partitions of n with strictly decreasing run-sums. - Gus Wiseman, Oct 21 2022
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 71 terms from Seiichi Manyama)
FORMULA
a(n) <= A304405(n).
EXAMPLE
n | | Sequence of the sum of the same summands
--+----------------------+-----------------------------------------
1 | 1 | 1
2 | 2 | 2
| 1+1 | 2
3 | 3 | 3
| 2+1 | 1, 2
| 1+1+1 | 3
4 | 4 | 4
| 3+1 | 1, 3
| 2+2 | 4
| 1+1+1+1 | 4
5 | 5 | 5
| 4+1 | 1, 4
| 3+2 | 2, 3
| 3+1+1 | 2, 3
| 2+2+1 | 1, 4
| 1+1+1+1+1 | 5
6 | 6 | 6
| 5+1 | 1, 5
| 4+2 | 2, 4
| 4+1+1 | 2, 4
| 3+3 | 6
| 3+2+1 | 1, 2, 3
| 2+2+2 | 6
| 2+2+1+1 | 2, 4
| 1+1+1+1+1+1 | 6
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Greater@@Total/@Split[#]&]], {n, 0, 30}] (* Gus Wiseman, Oct 21 2022 *)
CROSSREFS
Number of rows in A354584 summing to n that are strictly increasing.
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 12 2018
STATUS
approved