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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325552 Number of compositions of n with distinct differences up to sign. 6
1, 1, 2, 3, 6, 9, 12, 23, 38, 61, 78, 135, 194, 315, 454, 699, 982, 1495, 2102, 3085, 4406, 6583, 9048, 13117, 18540, 26399 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A composition of n is a finite sequence of positive integers summing to n.

The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (3,1,2) are (-2,1).

a(n) has the same parity as n for n > 0, since reversing a composition does not change whether or not it has this property, and the only valid symmetric compositions are (n) and (n/2,n/2), with the latter only existing for even n. - Charlie Neder, Jun 06 2019

LINKS

Table of n, a(n) for n=0..25.

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

EXAMPLE

The differences of (1,2,1) are (1,-1), which are different but not up to sign, so (1,2,1) is not counted under a(4).

The a(1) = 1 through a(7) = 23 compositions:

  (1)  (2)   (3)   (4)    (5)    (6)    (7)

       (11)  (12)  (13)   (14)   (15)   (16)

             (21)  (22)   (23)   (24)   (25)

                   (31)   (32)   (33)   (34)

                   (112)  (41)   (42)   (43)

                   (211)  (113)  (51)   (52)

                          (122)  (114)  (61)

                          (221)  (132)  (115)

                          (311)  (213)  (124)

                                 (231)  (133)

                                 (312)  (142)

                                 (411)  (214)

                                        (223)

                                        (241)

                                        (322)

                                        (331)

                                        (412)

                                        (421)

                                        (511)

                                        (1132)

                                        (2113)

                                        (2311)

                                        (3112)

MATHEMATICA

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Abs[Differences[#]]&]], {n, 0, 15}]

CROSSREFS

Cf. A000079, A070211, A175342, A242882, A325325, A325368, A325404, A325545, A325551, A325553, A325555, A325557.

Sequence in context: A058616 A298435 A261539 * A271882 A123316 A303365

Adjacent sequences:  A325549 A325550 A325551 * A325553 A325554 A325555

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 11 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 January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)