login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325551 Number of compositions of n with distinct circular differences. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A093903 A117128 A006509 * A258928 A144562 A102889

Adjacent sequences:  A325548 A325549 A325550 * A325552 A325553 A325554

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 10 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 7 16:09 EDT 2020. Contains 335496 sequences. (Running on oeis4.)