A325279 Number of integer partitions of n whose maximum multiplicity is one greater than their minimum multiplicity.

0, 0, 0, 0, 1, 2, 1, 5, 6, 9, 10, 18, 18, 31, 34, 48, 57, 80, 86, 122, 138, 183, 211, 275, 311, 402, 461, 576, 663, 825, 942, 1163, 1334, 1621, 1865, 2248, 2566, 3084, 3532, 4193, 4794, 5674, 6472, 7617, 8685, 10153, 11576, 13483, 15320, 17790, 20200, 23342

Offset

0,6

Comments

The Heinz numbers of these partitions are given by A325241.

For example, the partition (44111) has two multiplicities (2 and 3) which differ by 1, so is counted under a(11).

Links

Table of n, a(n) for n=0..51.

Example

The a(4) = 1 through a(11) = 18 partitions:
  (211)  (221)  (411)  (322)    (332)    (441)    (433)      (443)
         (311)         (331)    (422)    (522)    (442)      (533)
                       (511)    (611)    (711)    (622)      (551)
                       (3211)   (3221)   (3321)   (811)      (722)
                       (22111)  (4211)   (4221)   (5221)     (911)
                                (22211)  (4311)   (5311)     (4322)
                                         (5211)   (6211)     (4331)
                                         (32211)  (33211)    (4421)
                                         (33111)  (42211)    (5411)
                                                  (2221111)  (6221)
                                                             (6311)
                                                             (7211)
                                                             (33221)
                                                             (33311)
                                                             (43211)
                                                             (44111)
                                                             (52211)
                                                             (2222111)

Mathematica

Table[Length[Select[IntegerPartitions[n], Max@@Length/@Split[#]-Min@@Length/@Split[#]==1&]], {n, 0, 30}]

Crossrefs

Cf. A047966, A062770, A071625, A098859, A117571, A127002, A325242, A325244, A325245, A325280.

Sequence in context: A026214 A026221 A030740 * A095242 A357179 A125080

Adjacent sequences: A325276 A325277 A325278 * A325280 A325281 A325282

Keyword

nonn

Author

Gus Wiseman, Apr 18 2019

Status

approved