OFFSET
1,2
COMMENTS
A strict composition of k is a finite sequence of distinct positive integers summing to k.
FORMULA
Moebius transform is A032020 (strict compositions).
EXAMPLE
The a(1) = 1 through a(7) = 14 compositions:
(1) (1) (1) (1) (1) (1) (1)
(2) (3) (2) (5) (2) (7)
(1,2) (4) (1,4) (3) (1,6)
(2,1) (1,3) (2,3) (6) (2,5)
(3,1) (3,2) (1,2) (3,4)
(4,1) (1,5) (4,3)
(2,1) (5,2)
(2,4) (6,1)
(4,2) (1,2,4)
(5,1) (1,4,2)
(1,2,3) (2,1,4)
(1,3,2) (2,4,1)
(2,1,3) (4,1,2)
(2,3,1) (4,2,1)
(3,1,2)
(3,2,1)
MATHEMATICA
Table[Sum[Length[Join@@Permutations/@Select[IntegerPartitions[d], UnsameQ@@#&]], {d, Divisors[n]}], {n, 12}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 11 2020
STATUS
approved