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 A325556 Number of necklace compositions of n with distinct circular differences up to sign. 5
 1, 1, 1, 1, 1, 1, 3, 7, 9, 13, 25, 27, 51, 63, 95, 123, 179, 205, 305, 409, 559, 715, 1009, 1337, 1869 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS A necklace composition of n is a finite sequence of positive integers summing to n that is lexicographically minimal among all of its cyclic rotations. The circular differences of a composition c of length k are c_{i + 1} - c_i for i < k and c_1 - c_i for i = k. For example, the circular differences of (1,2,1,3) are (1,-1,2,-2). LINKS Table of n, a(n) for n=1..25. Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts. EXAMPLE The a(1) = 1 through a(10) = 13 necklace compositions: (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (124) (125) (126) (127) (142) (134) (162) (136) (143) (1125) (145) (152) (1134) (154) (1124) (1143) (163) (1142) (1152) (172) (1224) (235) (1422) (253) (1126) (1162) (1225) (1522) MATHEMATICA neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]; Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Abs[Differences[Append[#, First[#]]]]&&neckQ[#]&]], {n, 15}] CROSSREFS Cf. A000079, A000740, A008965, A235998, A318728, A325324, A325325, A325349, A325549, A325553, A325555, A325588, A325590. Sequence in context: A109370 A018663 A110575 * A174840 A032664 A166733 Adjacent sequences: A325553 A325554 A325555 * A325557 A325558 A325559 KEYWORD nonn,more AUTHOR Gus Wiseman, May 11 2019 STATUS approved

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Last modified August 14 19:51 EDT 2024. Contains 375167 sequences. (Running on oeis4.)