A337450 Number of relatively prime compositions of n with no 1's.

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

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.

Cf. A000010, A007359, A023023, A101268, A178472, A289509, A302568, A337485.

Sequence in context: A021486 A258990 A351727 * A228819 A104540 A178818

Adjacent sequences: A337447 A337448 A337449 * A337451 A337452 A337453

Keyword

nonn

Author

Gus Wiseman, Aug 31 2020

Status

approved