A325551 Number of compositions of n with distinct circular differences.

1, 1, 3, 6, 11, 8, 26, 50, 79, 121, 195, 265, 478, 742, 1269, 1914, 2929, 4462, 6825, 10309, 16324, 24633, 37213, 56828, 84482

Offset: 1

Author

Gus Wiseman, May 10 2019

Keywords

• nonn
• more

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), which are distinct, so (1,2,1,3) is counted under a(7).

Examples

			The a(1) = 1 through a(7) = 26 compositions:
  (1)  (2)  (3)   (4)    (5)    (6)    (7)
            (12)  (13)   (14)   (15)   (16)
            (21)  (31)   (23)   (24)   (25)
                  (112)  (32)   (42)   (34)
                  (121)  (41)   (51)   (43)
                  (211)  (113)  (114)  (52)
                         (122)  (141)  (61)
                         (131)  (411)  (115)
                         (212)         (124)
                         (221)         (133)
                         (311)         (142)
                                       (151)
                                       (214)
                                       (223)
                                       (232)
                                       (241)
                                       (313)
                                       (322)
                                       (331)
                                       (412)
                                       (421)
                                       (511)
                                       (1213)
                                       (1312)
                                       (2131)
                                       (3121)
		

Links

• Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Crossrefs

Cf. A000079, A000740, A008965, A242882, A325545, A325549, A325553, A325558, A325589, A325591.

Programs

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Differences[Append[#,First[#]]]&]],{n,15}]