OFFSET
0,4
COMMENTS
Moebius transform of A032020.
Ranking these compositions using standard compositions (A066099) gives the intersection of A233564 (strict) with A291166 (relatively prime). - Gus Wiseman, Oct 18 2020
LINKS
EXAMPLE
a(6) = 8 because we have [5, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 5], [1, 3, 2] and [1, 2, 3].
From Gus Wiseman, Oct 18 2020: (Start)
The a(1) = 1 through a(8) = 16 compositions (empty column indicated by dot):
(1) . (1,2) (1,3) (1,4) (1,5) (1,6) (1,7)
(2,1) (3,1) (2,3) (5,1) (2,5) (3,5)
(3,2) (1,2,3) (3,4) (5,3)
(4,1) (1,3,2) (4,3) (7,1)
(2,1,3) (5,2) (1,2,5)
(2,3,1) (6,1) (1,3,4)
(3,1,2) (1,2,4) (1,4,3)
(3,2,1) (1,4,2) (1,5,2)
(2,1,4) (2,1,5)
(2,4,1) (2,5,1)
(4,1,2) (3,1,4)
(4,2,1) (3,4,1)
(4,1,3)
(4,3,1)
(5,1,2)
(5,2,1)
(End)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@#&&GCD@@#<=1&]], {n, 0, 15}] (* Gus Wiseman, Oct 18 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 04 2020
STATUS
approved