A324520 Number of integer partitions of n > 0 where the minimum part equals the number of parts minus the number of distinct parts.

0, 1, 0, 1, 2, 2, 3, 3, 7, 6, 11, 12, 15, 21, 25, 31, 43, 49, 58, 79, 89, 108, 135, 165, 190, 232, 279, 328, 387, 461, 536, 650, 743, 870, 1029, 1202, 1381, 1613, 1864, 2163, 2505, 2875, 3292, 3829, 4367, 5001, 5746, 6538, 7462, 8533, 9714, 11008, 12527, 14196

Offset

1,5

Comments

The Heinz numbers of these integer partitions are given by A324519.

Links

Table of n, a(n) for n=1..54.

Example

The a(2) = 1 through a(11) = 11 integer partitions:
  (11)  (211)  (221)  (222)  (331)   (611)   (441)   (811)   (551)
               (311)  (411)  (511)   (3221)  (711)   (3322)  (911)
                             (3211)  (4211)  (3222)  (4222)  (3332)
                                             (3321)  (5221)  (4331)
                                             (4221)  (5311)  (4421)
                                             (4311)  (6211)  (5222)
                                             (5211)          (5411)
                                                             (6221)
                                                             (6311)
                                                             (7211)
                                                             (43211)

Mathematica

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

Crossrefs

Cf. A003114, A006141, A039900, A046660, A047993, A064174, A090858, A133121.

Cf. A324516, A324518, A324519, A324520.

Sequence in context: A162223 A133076 A295510 * A307737 A309684 A330950

Adjacent sequences: A324517 A324518 A324519 * A324521 A324522 A324523

Keyword

nonn

Author

Gus Wiseman, Mar 06 2019

Status

approved