This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325680 #13 Jun 19 2021 22:28:56
%S A325680 1,1,2,4,5,6,8,14,16,29,24,42,46,78,66,146,133,242,208,386,352,620,
%T A325680 494,948,842,1447
%N A325680 Number of compositions of n such that every distinct circular subsequence has a different sum.
%C A325680 A composition of n is a finite sequence of positive integers summing to n.
%C A325680 A circular subsequence is a sequence of consecutive terms where the first and last parts are also considered consecutive.
%e A325680 The a(1) = 1 through a(8) = 16 compositions:
%e A325680 (1) (2) (3) (4) (5) (6) (7) (8)
%e A325680 (11) (12) (13) (14) (15) (16) (17)
%e A325680 (21) (22) (23) (24) (25) (26)
%e A325680 (111) (31) (32) (33) (34) (35)
%e A325680 (1111) (41) (42) (43) (44)
%e A325680 (11111) (51) (52) (53)
%e A325680 (222) (61) (62)
%e A325680 (111111) (124) (71)
%e A325680 (142) (125)
%e A325680 (214) (152)
%e A325680 (241) (215)
%e A325680 (412) (251)
%e A325680 (421) (512)
%e A325680 (1111111) (521)
%e A325680 (2222)
%e A325680 (11111111)
%t A325680 subalt[q_]:=Union[ReplaceList[q,{___,s__,___}:>{s}],DeleteCases[ReplaceList[q,{t___,__,u___}:>{u,t}],{}]];
%t A325680 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Total/@subalt[#]&]],{n,0,15}]
%Y A325680 Cf. A000079, A008965, A108917, A143823, A169942, A276024.
%Y A325680 Cf. A325545, A325676, A325682, A325685, A325687, A325688.
%K A325680 nonn,more
%O A325680 0,3
%A A325680 _Gus Wiseman_, May 13 2019
%E A325680 a(18)-a(25) from _Robert Price_, Jun 19 2021