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A325875 Number of compositions of n whose differences of all degrees > 1 are nonzero. 7
1, 1, 2, 3, 7, 13, 20, 38, 69, 129, 222, 407, 726, 1313, 2318, 4146, 7432, 13296, 23759, 42458, 75714 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2). The zeroth differences are the sequence itself, while k-th differences for k > 0 are the differences of the (k-1)-th differences. If m is the length of the sequence, its differences of all degrees are the union of the zeroth through m-th differences.

A composition of n is a finite sequence of positive integers with sum n.

The case for all degrees including 1 is A325851.

LINKS

Table of n, a(n) for n=0..20.

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

EXAMPLE

The a(1) = 1 through a(6) = 20 compositions:

  (1)  (2)   (3)   (4)    (5)     (6)

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

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

                   (31)   (32)    (33)

                   (112)  (41)    (42)

                   (121)  (113)   (51)

                   (211)  (122)   (114)

                          (131)   (132)

                          (212)   (141)

                          (221)   (213)

                          (311)   (231)

                          (1121)  (312)

                          (1211)  (411)

                                  (1122)

                                  (1131)

                                  (1212)

                                  (1311)

                                  (2121)

                                  (2211)

                                  (11211)

MATHEMATICA

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !MemberQ[Union@@Table[Differences[#, i], {i, 2, Length[#]}], 0]&]], {n, 0, 10}]

CROSSREFS

Cf. A049988, A238423, A325325, A325468, A325545, A325849, A325850, A325851, A325852, A325874, A325876.

Sequence in context: A156300 A067834 A070754 * A049887 A048216 A003509

Adjacent sequences:  A325872 A325873 A325874 * A325876 A325877 A325878

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 02 2019

STATUS

approved

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Last modified April 6 11:51 EDT 2020. Contains 333273 sequences. (Running on oeis4.)