A324518 Number of integer partitions of n > 0 where the maximum part equals the length minus the number of distinct parts.

0, 1, 0, 0, 1, 2, 2, 0, 3, 1, 6, 7, 7, 9, 11, 10, 16, 26, 22, 42, 43, 54, 61, 83, 85, 118, 135, 179, 201, 263, 297, 371, 445, 510, 608, 732, 886, 1009, 1231, 1442, 1721, 2015, 2416, 2750, 3327, 3784, 4542, 5190, 6142, 7044, 8315, 9573, 11203, 12913, 15056

Offset

1,6

Comments

The Heinz numbers of these integer partitions are given by A324517.

Links

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

Example

The a(2) = 1 through a(12) = 7 integer partitions:
  (11)  (2111)  (222)   (2221)   (33111)   (322111)  (32222)    (3333)
                (2211)  (31111)  (321111)            (33311)    (33222)
                                 (411111)            (322211)   (322221)
                                                     (332111)   (332211)
                                                     (4211111)  (441111)
                                                     (5111111)  (4221111)
                                                                (4311111)

Mathematica

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

Crossrefs

Cf. A003114, A006141, A039900, A046660, A047993, A064174, A106529.

Cf. A324516, A324517, A324520, A324562.

Sequence in context: A248813 A235917 A093949 * A108807 A129236 A127465

Adjacent sequences: A324515 A324516 A324517 * A324519 A324520 A324521

Keyword

nonn

Author

Gus Wiseman, Mar 06 2019

Status

approved