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

1,3

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).

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(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)

Mathematica

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

Crossrefs

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

Sequence in context: A364054 A117128 A006509 * A258928 A144562 A102889

Adjacent sequences: A325548 A325549 A325550 * A325552 A325553 A325554

Keyword

nonn,more

Author

Gus Wiseman, May 10 2019

Status

approved