OFFSET
0,5
COMMENTS
A reversed integer partition of n is a finite weakly increasing sequence of positive integers summing to n.
EXAMPLE
The a(0) = 0 through a(8) = 14 partitions (empty column indicated by dot):
. (1) (11) (111) (13) (14) (15) (16) (17)
(22) (1112) (114) (115) (116)
(112) (11111) (222) (1123) (134)
(1111) (1113) (11113) (224)
(1122) (11122) (233)
(11112) (111112) (1115)
(111111) (1111111) (2222)
(11114)
(11123)
(11222)
(111113)
(111122)
(1111112)
(11111111)
For example, the reversed partition (2,2,4) has a unique fixed point at the second position.
MATHEMATICA
pq[y_]:=Length[Select[Range[Length[y]], #==y[[#]]&]];
Table[Length[Select[Reverse/@IntegerPartitions[n], pq[#]==1&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 08 2022
STATUS
approved