A337561 Number of pairwise coprime strict compositions of n, where a singleton is not considered coprime unless it is (1).

1, 1, 0, 2, 2, 4, 8, 6, 16, 12, 22, 40, 40, 66, 48, 74, 74, 154, 210, 228, 242, 240, 286, 394, 806, 536, 840, 654, 1146, 1618, 2036, 2550, 2212, 2006, 2662, 4578, 4170, 7122, 4842, 6012, 6214, 11638, 13560, 16488, 14738, 15444, 16528, 25006, 41002, 32802

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.

A000740 counts relatively prime compositions, with strict case A332004.

A051424 counts pairwise coprime or singleton partitions.

A101268 considers all singletons to be coprime, with strict case A337562.

A178472 counts compositions with a common factor > 1.

A327516 counts pairwise coprime partitions, with strict case A305713.

A328673 counts pairwise non-coprime partitions.

A333228 ranks compositions whose distinct parts are pairwise coprime.

Cf. A007359, A007360, A087087, A216652, A220377, A302569, A307719, A326675, A333227, A337461.

Sequence in context: A123958 A377231 A048572 * A121173 A160159 A283241

Adjacent sequences: A337558 A337559 A337560 * A337562 A337563 A337564

Keyword

nonn

Author

Gus Wiseman, Sep 18 2020

Status

approved