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 of a sequence are the sequence itself, while the k-th differences for k > 0 are the differences of the (k-1)-th differences.
The Heinz numbers of these partitions are given by A325399.
LINKS
EXAMPLE
The a(1) = 1 through a(9) = 5 partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(21) (31) (32) (42) (43) (53) (54)
(41) (51) (52) (62) (63)
(61) (71) (72)
(431) (81)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And@@Table[Greater@@Differences[#, k], {k, 0, Length[#]}]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 02 2019
STATUS
approved