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A325851 Number of (strict) compositions of n whose differences of all degrees are nonzero. 6
1, 1, 1, 3, 4, 7, 12, 21, 35, 58, 102, 171, 284, 485, 819, 1355, 2301, 3884, 6528, 10983, 18380, 30824, 51851 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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. The differences of all degrees of a sequence are the union of its zeroth through m-th differences, where m is the length of the sequence.

LINKS

Table of n, a(n) for n=0..22.

EXAMPLE

The a(1) = 1 through a(7) = 21 compositions:

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

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

            (21)  (31)   (23)   (24)    (25)

                  (121)  (32)   (42)    (34)

                         (41)   (51)    (43)

                         (131)  (132)   (52)

                         (212)  (141)   (61)

                                (213)   (124)

                                (231)   (142)

                                (312)   (151)

                                (1212)  (214)

                                (2121)  (232)

                                        (241)

                                        (313)

                                        (412)

                                        (421)

                                        (1213)

                                        (1312)

                                        (2131)

                                        (3121)

                                        (12121)

MATHEMATICA

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

CROSSREFS

The case for only degrees > 1 is A325875.

Cf. A049988, A175342, A238423, A295370, A325328, A325545, A325850, A325852, A325874.

Sequence in context: A293642 A214286 A108700 * A062202 A049859 A124636

Adjacent sequences:  A325848 A325849 A325850 * A325852 A325853 A325854

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 31 2019

STATUS

approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)