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 A325680 Number of compositions of n such that every distinct circular subsequence has a different sum. 13
 1, 1, 2, 4, 5, 6, 8, 14, 16, 29, 24, 42, 46, 78, 66, 146, 133, 242, 208, 386, 352, 620, 494, 948, 842, 1447 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A composition of n is a finite sequence of positive integers summing to n. A circular subsequence is a sequence of consecutive terms where the first and last parts are also considered consecutive. LINKS Table of n, a(n) for n=0..25. EXAMPLE The a(1) = 1 through a(8) = 16 compositions: (1) (2) (3) (4) (5) (6) (7) (8) (11) (12) (13) (14) (15) (16) (17) (21) (22) (23) (24) (25) (26) (111) (31) (32) (33) (34) (35) (1111) (41) (42) (43) (44) (11111) (51) (52) (53) (222) (61) (62) (111111) (124) (71) (142) (125) (214) (152) (241) (215) (412) (251) (421) (512) (1111111) (521) (2222) (11111111) MATHEMATICA subalt[q_]:=Union[ReplaceList[q, {___, s__, ___}:>{s}], DeleteCases[ReplaceList[q, {t___, __, u___}:>{u, t}], {}]]; Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Total/@subalt[#]&]], {n, 0, 15}] CROSSREFS Cf. A000079, A008965, A108917, A143823, A169942, A276024. Cf. A325545, A325676, A325682, A325685, A325687, A325688. Sequence in context: A270877 A303909 A110277 * A176654 A185867 A326910 Adjacent sequences: A325677 A325678 A325679 * A325681 A325682 A325683 KEYWORD nonn,more AUTHOR Gus Wiseman, May 13 2019 EXTENSIONS a(18)-a(25) from Robert Price, Jun 19 2021 STATUS approved

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Last modified October 4 22:13 EDT 2023. Contains 365888 sequences. (Running on oeis4.)