OFFSET
0,3
COMMENTS
The partition run-sum trajectory is obtained by repeatedly taking the run-sums until a strict partition is reached. For example, the trajectory of y = (3,2,1,1,1) is (3,2,1,1,1) -> (3,3,2) -> (6,2), so y is counted under T(8,2).
EXAMPLE
Triangle begins:
1
1
2
2 1
4 1
2 5
5 5 1
2 12 1
8 11 3
3 19 8
5 27 9 1
2 34 19 1
15 26 34 2
2 49 45 5
5 68 48 14
4 58 98 15 1
For example, row n = 8 counts the following partitions:
(8) (53) (431)
(44) (62) (521)
(422) (71) (3221)
(2222) (332)
(4211) (611)
(41111) (3311)
(221111) (5111)
(11111111) (22211)
(32111)
(311111)
(2111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[FixedPoint[Sort[Total/@Split[#]]&, #]]==k&]], {n, 0, 15}, {k, 0, n}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Jun 04 2022
STATUS
approved