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Number of pairwise coprime strict compositions of n, where a singleton is not considered coprime unless it is (1).
32

%I #13 Jan 19 2021 01:09:01

%S 1,1,0,2,2,4,8,6,16,12,22,40,40,66,48,74,74,154,210,228,242,240,286,

%T 394,806,536,840,654,1146,1618,2036,2550,2212,2006,2662,4578,4170,

%U 7122,4842,6012,6214,11638,13560,16488,14738,15444,16528,25006,41002,32802

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

%H Fausto A. C. Cariboni, <a href="/A337561/b337561.txt">Table of n, a(n) for n = 0..600</a>

%F a(n) = A337562(n) - 1 for n > 1.

%e The a(1) = 1 through a(9) = 12 compositions (empty column shown as dot):

%e (1) . (1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8)

%e (2,1) (3,1) (2,3) (5,1) (2,5) (3,5) (2,7)

%e (3,2) (1,2,3) (3,4) (5,3) (4,5)

%e (4,1) (1,3,2) (4,3) (7,1) (5,4)

%e (2,1,3) (5,2) (1,2,5) (7,2)

%e (2,3,1) (6,1) (1,3,4) (8,1)

%e (3,1,2) (1,4,3) (1,3,5)

%e (3,2,1) (1,5,2) (1,5,3)

%e (2,1,5) (3,1,5)

%e (2,5,1) (3,5,1)

%e (3,1,4) (5,1,3)

%e (3,4,1) (5,3,1)

%e (4,1,3)

%e (4,3,1)

%e (5,1,2)

%e (5,2,1)

%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],#=={}||UnsameQ@@#&&CoprimeQ@@#&]],{n,0,10}]

%Y A072706 counts unimodal strict compositions.

%Y A220377*6 counts these compositions of length 3.

%Y A305713 is the unordered version.

%Y A337462 is the not necessarily strict version.

%Y A000740 counts relatively prime compositions, with strict case A332004.

%Y A051424 counts pairwise coprime or singleton partitions.

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

%Y A178472 counts compositions with a common factor > 1.

%Y A327516 counts pairwise coprime partitions, with strict case A305713.

%Y A328673 counts pairwise non-coprime partitions.

%Y A333228 ranks compositions whose distinct parts are pairwise coprime.

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

%K nonn

%O 0,4

%A _Gus Wiseman_, Sep 18 2020