login
A325468
Number of integer partitions y of n such that the k-th differences of y are distinct (independently) for all k >= 0.
14
1, 1, 1, 2, 2, 3, 3, 5, 6, 6, 9, 11, 10, 15, 17, 19, 24, 31, 26, 40, 43, 51, 52, 72, 66, 89, 88, 111, 119, 150, 130, 183, 193, 229, 231, 279, 287, 358, 365, 430, 426, 538, 535, 649, 680, 742, 803, 943, 982, 1136, 1115
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 A325467.
EXAMPLE
The a(1) = 1 through a(9) = 6 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)
(421) (431) (81)
(521) (621)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And@@Table[UnsameQ@@Differences[#, k], {k, 0, Length[#]}]&]], {n, 0, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 03 2019
STATUS
approved