OFFSET
0,5
COMMENTS
A nonfixed point in a composition c is an index i such that c_i != i.
EXAMPLE
Triangle begins:
1
1 0
0 2 0
1 1 2 0
0 4 2 2 0
0 5 5 4 2 0
1 3 12 8 6 2 0
0 7 14 19 14 8 2 0
0 8 21 33 32 22 10 2 0
0 9 30 54 63 54 32 12 2 0
1 6 47 80 116 116 86 44 14 2 0
For example, row n = 6 counts the following compositions (empty column indicated by dot):
(123) (6) (24) (231) (2112) (21111) .
(15) (33) (312) (2121) (111111)
(42) (51) (411) (3111)
(114) (1113) (11112)
(132) (1122) (11121)
(141) (1311) (11211)
(213) (2211)
(222) (12111)
(321)
(1131)
(1212)
(1221)
MATHEMATICA
pnq[y_]:=Length[Select[Range[Length[y]], #!=y[[#]]&]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], pnq[#]==k&]], {n, 0, 9}, {k, 0, n}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2022
STATUS
approved