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) (with the last part taken to be 0) are (-3,-2,-1).
The Heinz numbers of these partitions are given by A325367.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400
EXAMPLE
The a(1) = 1 through a(11) = 15 partitions (A = 10, B = 11):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
(11) (22) (32) (33) (43) (44) (54) (55) (65)
(31) (41) (51) (52) (53) (72) (64) (74)
(311) (411) (61) (62) (81) (73) (83)
(322) (71) (441) (82) (92)
(331) (332) (522) (91) (A1)
(511) (611) (711) (433) (443)
(622) (533)
(631) (551)
(811) (632)
(641)
(722)
(731)
(911)
(6311)
For example, (6,3,1,1) has differences (-3,-2,0,-1), which are distinct, so (6,3,1,1) is counted under a(11).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@Differences[Append[#, 0]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 23 2019
STATUS
approved