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A325553 Number of compositions of n with distinct circular differences up to sign. 7
1, 1, 1, 1, 1, 1, 7, 21, 31, 41, 87, 99, 191, 245, 381, 501, 735, 883, 1309, 1841, 2589, 3435, 4941, 6857, 9791 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

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).

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(8) = 21 compositions:

  (1)  (2)  (3)  (4)  (5)  (6)  (7)    (8)

                                (124)  (125)

                                (142)  (134)

                                (214)  (143)

                                (241)  (152)

                                (412)  (215)

                                (421)  (251)

                                       (314)

                                       (341)

                                       (413)

                                       (431)

                                       (512)

                                       (521)

                                       (1124)

                                       (1142)

                                       (1241)

                                       (1421)

                                       (2114)

                                       (2411)

                                       (4112)

                                       (4211)

MATHEMATICA

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Abs[Differences[Append[#, First[#]]]]&]], {n, 20}]

CROSSREFS

Cf. A000079, A008965, A167606, A173258, A325324, A325349, A325545, A325549, A325551, A325552, A325553, A325556, A325558.

Sequence in context: A160890 A319527 A297178 * A032639 A264619 A015729

Adjacent sequences:  A325550 A325551 A325552 * A325554 A325555 A325556

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 11 2019

STATUS

approved

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Last modified June 4 11:32 EDT 2020. Contains 334825 sequences. (Running on oeis4.)