|
%I #13 Oct 21 2020 22:49:35
%S 1,1,0,2,2,4,8,12,16,24,52,64,88,132,180,344,416,616,816,1176,1496,
%T 2736,3232,4756,6176,8756,11172,15576,24120,30460,41456,55740,74440,
%U 97976,130192,168408,256464,315972,429888,558192,749920,958264,1274928,1621272,2120288,3020256
%N Number of compositions (ordered partitions) of n into distinct and relatively prime parts.
%C Moebius transform of A032020.
%C Ranking these compositions using standard compositions (A066099) gives the intersection of A233564 (strict) with A291166 (relatively prime). - _Gus Wiseman_, Oct 18 2020
%H Alois P. Heinz, <a href="/A332004/b332004.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e a(6) = 8 because we have [5, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 5], [1, 3, 2] and [1, 2, 3].
%e From _Gus Wiseman_, Oct 18 2020: (Start)
%e The a(1) = 1 through a(8) = 16 compositions (empty column indicated by dot):
%e (1) . (1,2) (1,3) (1,4) (1,5) (1,6) (1,7)
%e (2,1) (3,1) (2,3) (5,1) (2,5) (3,5)
%e (3,2) (1,2,3) (3,4) (5,3)
%e (4,1) (1,3,2) (4,3) (7,1)
%e (2,1,3) (5,2) (1,2,5)
%e (2,3,1) (6,1) (1,3,4)
%e (3,1,2) (1,2,4) (1,4,3)
%e (3,2,1) (1,4,2) (1,5,2)
%e (2,1,4) (2,1,5)
%e (2,4,1) (2,5,1)
%e (4,1,2) (3,1,4)
%e (4,2,1) (3,4,1)
%e (4,1,3)
%e (4,3,1)
%e (5,1,2)
%e (5,2,1)
%e (End)
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@#&&GCD@@#<=1&]],{n,0,15}] (* _Gus Wiseman_, Oct 18 2020 *)
%Y Cf. A007360, A032020, A108700, A302698.
%Y A000740 is the non-strict version.
%Y A078374 is the unordered version (non-strict: A000837).
%Y A101271*6 counts these compositions of length 3 (non-strict: A000741).
%Y A337561/A337562 is the pairwise coprime instead of relatively prime version (non-strict: A337462/A101268).
%Y A289509 gives the Heinz numbers of relatively prime partitions.
%Y A333227/A335235 ranks pairwise coprime compositions.
%Y Cf. A001523, A178472, A216652, A289508, A291166, A333228.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Feb 04 2020
|
