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A337450 Number of relatively prime compositions of n with no 1's. 11
0, 0, 0, 0, 0, 2, 0, 7, 5, 17, 17, 54, 51, 143, 168, 358, 482, 986, 1313, 2583, 3663, 6698, 9921, 17710, 26489, 46352, 70928, 121137, 188220, 317810, 497322, 832039, 1313501, 2177282, 3459041, 5702808, 9094377, 14930351, 23895672, 39084070, 62721578 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
A composition of n is a finite sequence of positive integers summing to n.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 171 terms from Fausto A. C. Cariboni)
EXAMPLE
The a(5) = 2 through a(10) = 17 compositions (empty column indicated by dot):
(2,3) . (2,5) (3,5) (2,7) (3,7)
(3,2) (3,4) (5,3) (4,5) (7,3)
(4,3) (2,3,3) (5,4) (2,3,5)
(5,2) (3,2,3) (7,2) (2,5,3)
(2,2,3) (3,3,2) (2,2,5) (3,2,5)
(2,3,2) (2,3,4) (3,3,4)
(3,2,2) (2,4,3) (3,4,3)
(2,5,2) (3,5,2)
(3,2,4) (4,3,3)
(3,4,2) (5,2,3)
(4,2,3) (5,3,2)
(4,3,2) (2,2,3,3)
(5,2,2) (2,3,2,3)
(2,2,2,3) (2,3,3,2)
(2,2,3,2) (3,2,2,3)
(2,3,2,2) (3,2,3,2)
(3,2,2,2) (3,3,2,2)
MAPLE
b:= proc(n, g) option remember; `if`(n=0,
`if`(g=1, 1, 0), add(b(n-j, igcd(g, j)), j=2..n))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..42);
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !MemberQ[#, 1]&&GCD@@#==1&]], {n, 0, 15}]
CROSSREFS
A000740 is the version allowing 1's.
2*A055684(n) is the case of length 2.
A302697 ranks the unordered case.
A302698 is the unordered version.
A337451 is the strict version.
A337452 is the unordered strict version.
A000837 counts relatively prime partitions.
A002865 counts partitions with no 1's.
A101268 counts singleton or pairwise coprime compositions.
A212804 counts compositions with no 1's.
A291166 appears to rank relatively prime compositions.
A337462 counts pairwise coprime compositions.
Sequence in context: A021486 A258990 A351727 * A228819 A104540 A178818
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 31 2020
STATUS
approved

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)