A325551 - OEIS

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

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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