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A317546 Number of multimin partitions of integer partitions of n. 14
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A036884 A102291 A034691 * A319001 A036669 A000633
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 31 2018
STATUS
approved

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Last modified June 13 00:51 EDT 2024. Contains 373362 sequences. (Running on oeis4.)