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

Author

Gus Wiseman, Apr 23 2019

Keywords

• nonn

Comments

The Heinz numbers of these partitions are given by A325368.

Examples

			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).
		

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.

Crossrefs

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

Programs

Mathematica

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