OFFSET
0,4
COMMENTS
If x and y are strict partitions of the same integer and it is possible to produce x by further partitioning the parts of y, flattening, and sorting, then x <= y.
This sequence is dominated by A294617 (set partitions of strict partitions).
LINKS
Robert Price, Table of n, a(n) for n = 0..70
EXAMPLE
The a(9) = 24 refinement-ordered pairs:
(9)<=(9)
(5,4)<=(9) (5,4)<=(5,4)
(6,3)<=(9) (6,3)<=(6,3)
(7,2)<=(9) (7,2)<=(7,2)
(8,1)<=(9) (8,1)<=(8,1)
(4,3,2)<=(9) (4,3,2)<=(5,4) (4,3,2)<=(6,3) (4,3,2)<=(7,2) (4,3,2)<=(4,3,2)
(5,3,1)<=(9) (5,3,1)<=(5,4) (5,3,1)<=(6,3) (5,3,1)<=(8,1) (5,3,1)<=(5,3,1)
(6,2,1)<=(9) (6,2,1)<=(6,3) (6,2,1)<=(7,2) (6,2,1)<=(8,1) (6,2,1)<=(6,2,1)
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
Table[Sum[Length[Union[Select[Sort/@Map[Total, mps[ptn], {2}], UnsameQ@@#&]]], {ptn, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 22 2018
STATUS
approved
