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Number of compositions of n such that every restriction to a circular subinterval has a different sum.
7

%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