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.
The case for all degrees including 1 is A325852.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..220
EXAMPLE
The a(1) = 1 through a(9) = 13 partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(11) (21) (22) (32) (33) (43) (44) (54)
(31) (41) (42) (52) (53) (63)
(211) (221) (51) (61) (62) (72)
(311) (411) (322) (71) (81)
(2211) (331) (332) (441)
(421) (422) (522)
(511) (431) (621)
(521) (711)
(611) (4221)
(3221) (4311)
(3311) (5211)
(32211)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !MemberQ[Union@@Table[Differences[#, i], {i, 2, Length[#]}], 0]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2019
STATUS
approved