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

1,4

Comments

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

Links

Table of n, a(n) for n=1..55.

Example

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)

Mathematica

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

Crossrefs

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

Cf. A324515, A324518, A324520.

Sequence in context: A224254 A107604 A080647 * A181058 A301452 A322788

Adjacent sequences: A324513 A324514 A324515 * A324517 A324518 A324519

Keyword

nonn

Author

Gus Wiseman, Mar 06 2019

Status

approved