A317546 Number of multimin partitions of integer partitions of n.

1, 3, 7, 18, 42, 104, 246, 594, 1416, 3391, 8084, 19312, 46041, 109829, 261827, 624254, 1487981, 3546883, 8453770, 20149014, 48021864, 114451536, 272769936, 650084053, 1549312743

Offset

1,2

Comments

A multimin partition of m is an ordered multiset partition of m such that the minima of the blocks are weakly increasing.

Links

Table of n, a(n) for n=1..25.

Formula

a(n) = Sum_{k > 0 : A056239(k) = n} A317545(k).

Example

The a(3) = 7 multimin partitions of integer partitions of 3:
  (3),
  (1)(2), (12),
  (1)(1)(1), (1)(11), (11)(1), (111).
The a(4) = 18 multimin partitions of integer partitions of 4:
  (4),
  (1)(3), (13),
  (2)(2), (22),
  (1)(1)(2), (1)(12), (11)(2), (12)(1), (112),
  (1)(1)(1)(1), (1)(1)(11), (1)(11)(1), (1)(111), (11)(1)(1), (11)(11), (111)(1), (1111).

Mathematica

mmcount[m_List]:=mmcount[m]=If[Length[m]===0, 0, 1+Plus@@mmcount/@Union[Subsets[Rest[m]]]];
Table[Sum[mmcount[Reverse[ptn]], {ptn, IntegerPartitions[n]}], {n, 25}]

Crossrefs

Cf. A007716, A020639, A034691, A255397, A300335, A317545.

Sequence in context: A036884 A102291 A034691 * A319001 A036669 A000633

Adjacent sequences: A317543 A317544 A317545 * A317547 A317548 A317549

Keyword

nonn

Author

Gus Wiseman, Jul 31 2018

Status

approved