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
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
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 02 2019
STATUS
approved