OFFSET
0,4
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600
FORMULA
a(n) = A337562(n) - 1 for n > 1.
EXAMPLE
The a(1) = 1 through a(9) = 12 compositions (empty column shown as dot):
(1) . (1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8)
(2,1) (3,1) (2,3) (5,1) (2,5) (3,5) (2,7)
(3,2) (1,2,3) (3,4) (5,3) (4,5)
(4,1) (1,3,2) (4,3) (7,1) (5,4)
(2,1,3) (5,2) (1,2,5) (7,2)
(2,3,1) (6,1) (1,3,4) (8,1)
(3,1,2) (1,4,3) (1,3,5)
(3,2,1) (1,5,2) (1,5,3)
(2,1,5) (3,1,5)
(2,5,1) (3,5,1)
(3,1,4) (5,1,3)
(3,4,1) (5,3,1)
(4,1,3)
(4,3,1)
(5,1,2)
(5,2,1)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], #=={}||UnsameQ@@#&&CoprimeQ@@#&]], {n, 0, 10}]
CROSSREFS
A072706 counts unimodal strict compositions.
A220377*6 counts these compositions of length 3.
A305713 is the unordered version.
A337462 is the not necessarily strict version.
A051424 counts pairwise coprime or singleton partitions.
A178472 counts compositions with a common factor > 1.
A328673 counts pairwise non-coprime partitions.
A333228 ranks compositions whose distinct parts are pairwise coprime.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 18 2020
STATUS
approved