%I #5 May 14 2019 22:07:30
%S 1,1,1,3,3,5,5,13,13,27,21,41,41,77,63,143,129,241,203,385,347
%N Number of compositions of n such that every restriction to a circular subinterval has a different sum.
%C A composition of n is a finite sequence of positive integers summing to n.
%C A circular subinterval is a sequence of consecutive indices where the first and last indices are also considered consecutive.
%e The a(1) = 1 through a(8) = 13 compositions:
%e (1) (2) (3) (4) (5) (6) (7) (8)
%e (12) (13) (14) (15) (16) (17)
%e (21) (31) (23) (24) (25) (26)
%e (32) (42) (34) (35)
%e (41) (51) (43) (53)
%e (52) (62)
%e (61) (71)
%e (124) (125)
%e (142) (152)
%e (214) (215)
%e (241) (251)
%e (412) (512)
%e (421) (521)
%t suball[q_]:=Join[Take[q,#]&/@Select[Tuples[Range[Length[q]],2],OrderedQ],Drop[q,#]&/@Select[Tuples[Range[2,Length[q]-1],2],OrderedQ]];
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Total/@suball[#]&]],{n,0,15}]
%Y Cf. A000079, A008965, A108917, A143823, A169942, A276024.
%Y Cf. A325545, A325676, A325677, A325678, A325680, A325681, A325687.
%K nonn,more
%O 0,4
%A _Gus Wiseman_, May 13 2019