

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
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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



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.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



