OFFSET
1,4
EXAMPLE
Triangle begins:
1
1 1
2 1
2 3
4 2 1
5 4 2
7 6 2
10 6 6
15 7 7 1
18 14 7 3
26 15 11 4
35 17 19 6
47 24 19 11
61 33 22 18 1
80 44 28 20 4
For example, row n = 9 counts the following reversed partitions:
(1134) (9) (27) (234)
(1224) (18) (36)
(1233) (117) (45)
(11115) (126) (135)
(11124) (1116) (144)
(11133) (1125) (225)
(11223) (2223) (333)
(12222)
(111114)
(111123)
(111222)
(1111113)
(1111122)
(11111112)
(111111111)
MATHEMATICA
partsabove[y_]:=Length[Select[Range[Length[y]], #<y[[#]]&]];
DeleteCases[Table[Length[Select[Reverse/@IntegerPartitions[n], partsabove[#]==k&]], {n, 1, 30}, {k, 0, n-1}], 0, 2]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 21 2022
STATUS
approved