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%I #28 Feb 01 2021 17:50:33
%S 0,0,0,0,0,2,0,4,2,10,8,20,14,34,52,72,90,146,172,244,390,502,680,956,
%T 1218,1686,2104,3436,4078,5786,7200,10108,12626,17346,20876,32836,
%U 38686,53674,67144,91528,113426,152810,189124,245884,343350,428494,552548,719156
%N Number of relatively prime strict compositions of n with no 1's.
%C A strict composition of n is a finite sequence of distinct positive integers summing to n.
%H Fausto A. C. Cariboni, <a href="/A337451/b337451.txt">Table of n, a(n) for n = 0..350</a>
%e The a(5) = 2 through a(10) = 8 compositions (empty column indicated by dot):
%e (2,3) . (2,5) (3,5) (2,7) (3,7)
%e (3,2) (3,4) (5,3) (4,5) (7,3)
%e (4,3) (5,4) (2,3,5)
%e (5,2) (7,2) (2,5,3)
%e (2,3,4) (3,2,5)
%e (2,4,3) (3,5,2)
%e (3,2,4) (5,2,3)
%e (3,4,2) (5,3,2)
%e (4,2,3)
%e (4,3,2)
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@#&&!MemberQ[#,1]&&GCD@@#==1&]],{n,0,15}]
%Y A032022 does not require relative primality.
%Y A302698 is the unordered non-strict version.
%Y A332004 is the version allowing 1's.
%Y A337450 is the non-strict version.
%Y A337452 is the unordered version.
%Y A000837 counts relatively prime partitions.
%Y A032020 counts strict compositions.
%Y A078374 counts strict relatively prime partitions.
%Y A002865 counts partitions with no 1's.
%Y A212804 counts compositions with no 1's.
%Y A291166 appears to rank relatively prime compositions.
%Y A337462 counts pairwise coprime compositions.
%Y A337561 counts strict pairwise coprime compositions.
%Y Cf. A000010, A007359, A101268, A178472, A216652, A289509, A337562, A337563.
%K nonn
%O 0,6
%A _Gus Wiseman_, Aug 31 2020
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