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A325553
Number of compositions of n with distinct circular differences up to sign.
7
1, 1, 1, 1, 1, 1, 1, 7, 21, 31, 41, 87, 99, 191, 245, 381, 501, 735, 883, 1309, 1841, 2589, 3435, 4941, 6857, 9791, 13503, 19475, 27073, 37175, 52299, 72249, 100359, 139317, 190549, 256769, 355193, 471963, 644433, 858793, 1159161, 1530879, 2056073, 2711921
OFFSET
0,8
COMMENTS
A composition of n is a finite sequence of positive integers summing to n.
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).
EXAMPLE
The a(1) = 1 through a(8) = 21 compositions:
(1) (2) (3) (4) (5) (6) (7) (8)
(124) (125)
(142) (134)
(214) (143)
(241) (152)
(412) (215)
(421) (251)
(314)
(341)
(413)
(431)
(512)
(521)
(1124)
(1142)
(1241)
(1421)
(2114)
(2411)
(4112)
(4211)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Abs[Differences[Append[#, First[#]]]]&]], {n, 20}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 11 2019
EXTENSIONS
a(0) and a(26)-a(43) from Alois P. Heinz, Jan 28 2024
STATUS
approved