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A319003 Number of ordered multiset partitions of integer partitions of n where the sequence of LCMs of the blocks is weakly increasing. 3
1, 3, 7, 17, 38, 87, 191, 420, 908, 1954 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If we form a multiorder by treating integer partitions (a,...,z) as multiarrows LCM(a,...,z) <= {z,...,a}, then a(n) is the number of triangles of weight n.

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

The a(4) = 17 ordered multiset partitions:

  {{4}}   {{1,3}}    {{2,2}}     {{1,1,2}}      {{1,1,1,1}}

         {{1},{3}}  {{2},{2}}   {{1},{1,2}}    {{1},{1,1,1}}

                                {{1,1},{2}}    {{1,1,1},{1}}

                               {{1},{1},{2}}   {{1,1},{1,1}}

                                               {{1},{1},{1,1}}

                                               {{1},{1,1},{1}}

                                               {{1,1},{1},{1}}

                                              {{1},{1},{1},{1}}

CROSSREFS

Cf. A000837, A007716, A063834, A269134, A290103, A316222, A317545, A317546, A319001, A319004.

Sequence in context: A178155 A026396 A176502 * A141199 A003478 A119587

Adjacent sequences:  A319000 A319001 A319002 * A319004 A319005 A319006

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 07 2018

STATUS

approved

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Last modified November 14 19:55 EST 2019. Contains 329128 sequences. (Running on oeis4.)