A325325 Number of integer partitions of n with distinct differences between successive parts.

1, 1, 2, 2, 4, 5, 5, 8, 11, 12, 16, 22, 21, 30, 34, 42, 49, 64, 67, 87, 95, 117, 132, 160, 169, 207, 230, 274, 301, 360, 395, 463, 506, 602, 656, 762, 834, 960, 1042, 1220, 1311, 1505, 1643, 1859, 2000, 2341, 2491, 2827, 3083, 3464, 3747, 4302, 4561, 5154

Offset

0,3

Comments

The Heinz numbers of these partitions are given by A325368.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400 (terms 0..123 from Alois P. Heinz)

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Example

The a(0) = 1 through a(9) = 12 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)
                                            (331)  (332)   (441)
                                            (421)  (422)   (522)
                                            (511)  (431)   (621)
                                                   (521)   (711)
                                                   (611)   (4221)
                                                   (4211)  (4311)
                                                           (5211)
For example, (5,2,1,1) has differences (-3,-1,0), which are distinct, so (5,2,1,1) is counted under a(9).

Mathematica

Table[Length[Select[IntegerPartitions[n], UnsameQ@@Differences[#]&]], {n, 0, 30}]

Crossrefs

Cf. A007294, A007862, A049988, A098859, A240026, A240027, A320348, A320466, A320470, A325324, A325349, A325352, A325368, A325404, A325468.

Sequence in context: A114701 A349464 A325260 * A240851 A261665 A208096

Adjacent sequences: A325322 A325323 A325324 * A325326 A325327 A325328

Keyword

nonn

Author

Gus Wiseman, Apr 23 2019

Status

approved