OFFSET
0,5
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000
EXAMPLE
The a(3) = 1 through a(9) = 9 triples:
(1,1,1) (1,1,2) (1,1,3) (1,1,4) (1,1,5) (1,1,6) (1,1,7)
(1,2,1) (1,3,1) (1,2,3) (1,5,1) (1,2,5) (1,3,5)
(2,1,1) (3,1,1) (1,3,2) (5,1,1) (1,3,4) (1,5,3)
(1,4,1) (1,4,3) (1,7,1)
(2,1,3) (1,5,2) (3,1,5)
(2,3,1) (1,6,1) (3,5,1)
(3,1,2) (2,1,5) (5,1,3)
(3,2,1) (2,5,1) (5,3,1)
(4,1,1) (3,1,4) (7,1,1)
(3,4,1)
(4,1,3)
(4,3,1)
(5,1,2)
(5,2,1)
(6,1,1)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n, {3}], CoprimeQ@@#&]], {n, 0, 30}]
CROSSREFS
A000212 counts the unimodal instead of coprime version.
A220377*6 is the strict case.
A307719 is the unordered version.
A337462 counts these compositions of any length.
A337563 counts the case of partitions with no 1's.
A337603 only requires the *distinct* parts to be pairwise coprime.
A337604 is the intersecting instead of coprime version.
A014612 ranks 3-part partitions.
A302696 ranks pairwise coprime partitions.
A327516 counts pairwise coprime partitions.
A333228 ranks compositions whose distinct parts are pairwise coprime.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 02 2020
STATUS
approved