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.
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
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 31 2019
STATUS
approved