A324516 Number of integer partitions of n > 0 where the maximum part minus the minimum part equals the length minus the number of distinct parts.

1, 1, 1, 2, 2, 2, 2, 5, 2, 8, 6, 6, 10, 14, 12, 20, 27, 23, 40, 40, 51, 62, 82, 88, 123, 135, 173, 197, 253, 285, 350, 419, 497, 594, 708, 855, 978, 1195, 1395, 1648, 1915, 2313, 2625, 3170, 3625, 4336, 4948, 5900, 6751, 7970, 9180, 10704, 12337, 14436, 16517

Offset: 1

Author

Gus Wiseman, Mar 06 2019

Keywords

• nonn

Comments

The Heinz numbers of these integer partitions are given by A324515.

Examples

			The a(8) = 5 through a(14) = 14 integer partitions:
  (8)      (9)      (A)       (B)       (C)        (D)        (E)
  (332)    (32211)  (433)     (443)     (4422)     (544)      (554)
  (3311)            (3331)    (33221)   (33321)    (43222)    (4442)
  (32111)           (4222)    (44111)   (422211)   (52222)    (5333)
  (41111)           (32221)   (422111)  (5211111)  (422221)   (43322)
                    (33211)   (431111)  (6111111)  (433111)   (44411)
                    (421111)                       (442111)   (442211)
                    (511111)                       (4321111)  (443111)
                                                   (5221111)  (551111)
                                                   (5311111)  (4322111)
                                                              (5222111)
                                                              (5411111)
                                                              (62111111)
                                                              (71111111)
		

Crossrefs

Cf. A006141, A039900, A046660, A047993, A064174, A243055.

Cf. A324515, A324518, A324520.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],Max@@#-Min@@#==Length[#]-Length[Union[#]]&]],{n,30}]