

A279375


Number of set partitions of strict integer partitions of n that have distinct blocksums.


17



1, 1, 1, 3, 3, 5, 9, 12, 16, 24, 39, 49, 70, 94, 127, 202, 247, 340, 450, 606, 772, 1169, 1407, 1920, 2454, 3267, 4089, 5469, 7293, 9222, 11884, 15291, 19417, 24890, 31469, 39662, 52619, 64764, 82502, 103576, 131169, 162726, 206015, 254233, 318464, 406262, 499210, 620593, 773673, 957073, 1181593
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

Also twice partitioned numbers where all partitions are strict. Also triangles of weight n in the multisystem of strict partitions. Strict partitions are an example of a multisystem that is neither transitive nor partitive nor contractible but is decomposable; see link for details.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100
Gus Wiseman, Comcategories and Multiorders (pdf version)


EXAMPLE

The a(6)=9 set partitions of strict integer partitions of 6 are: ((6)), ((51)), ((5)(1)), ((42)), ((4)(2)), ((321)), ((32)(1)), ((31)(2)), ((3)(2)(1)). The set partition ((3)(21)) is not counted because its blocks do not have distinct sums.


MATHEMATICA

nn=20; sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Total[Length[Select[sps[Sort[#]], UnsameQ@@Total/@#&]]&/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, nn}]


CROSSREFS

Cf. A063834, A089259, A258466, A270995, A271619, A275780, A279374.
Sequence in context: A159284 A078028 A317142 * A245143 A104220 A321986
Adjacent sequences: A279372 A279373 A279374 * A279376 A279377 A279378


KEYWORD

nonn


AUTHOR

Gus Wiseman, Dec 11 2016


STATUS

approved



