A323531 Number of square multiset partitions of integer partitions of n.

1, 1, 1, 1, 2, 2, 4, 5, 9, 12, 18, 24, 36, 48, 69, 97, 139, 196, 283, 402, 576, 819, 1161, 1635, 2301, 3209, 4469, 6193, 8571, 11812, 16291, 22404, 30850, 42414, 58393, 80305, 110578, 152091, 209308, 287686, 395352, 542413, 743603, 1017489, 1390510, 1896482

Offset

0,5

Comments

A multiset partition is square if the number of parts is equal to the number of parts in each part.

Links

Table of n, a(n) for n=0..45.

Example

The a(3) = 1 through a(9) = 12 square multiset partitions:
  (3)  (4)       (5)       (6)       (7)       (8)       (9)
       (11)(11)  (21)(11)  (21)(21)  (22)(21)  (22)(22)  (32)(22)
                           (22)(11)  (31)(21)  (31)(22)  (32)(31)
                           (31)(11)  (32)(11)  (31)(31)  (33)(21)
                                     (41)(11)  (32)(21)  (41)(22)
                                               (33)(11)  (41)(31)
                                               (41)(21)  (42)(21)
                                               (42)(11)  (43)(11)
                                               (51)(11)  (51)(21)
                                                         (52)(11)
                                                         (61)(11)
                                                         (111)(111)(111)

Mathematica

Table[Sum[Length[Union@@(Union[Sort/@Tuples[IntegerPartitions[#, {k}]&/@#]]&/@IntegerPartitions[n, {k}])], {k, Sqrt[n]}], {n, 30}]

Crossrefs

Cf. A000219, A001970, A047968, A261049, A279787, A305551, A319066, A323580.

Sequence in context: A038000 A089935 A204856 * A124280 A088518 A001224

Adjacent sequences: A323528 A323529 A323530 * A323532 A323533 A323534

Keyword

nonn

Author

Gus Wiseman, Jan 21 2019

Status

approved