OFFSET
1,2
COMMENTS
A multiset partition is uniform if all parts have the same size.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..482 (rows 1..100)
EXAMPLE
Triangle begins:
1
2 2
2 2
5 4 3
2 2
27 11 6 4
2 2
142 29 8 4
282 12 3
1073 101 8 4
The multiset partitions counted under row 6:
{123456} {112233} {111222} {111111}
{123}{456} {112}{233} {111}{222} {111}{111}
{124}{356} {113}{223} {112}{122} {11}{11}{11}
{125}{346} {122}{133} {11}{12}{22} {1}{1}{1}{1}{1}{1}
{126}{345} {123}{123} {12}{12}{12}
{134}{256} {11}{22}{33} {1}{1}{1}{2}{2}{2}
{135}{246} {11}{23}{23}
{136}{245} {12}{12}{33}
{145}{236} {12}{13}{23}
{146}{235} {13}{13}{22}
{156}{234} {1}{1}{2}{2}{3}{3}
{12}{34}{56}
{12}{35}{46}
{12}{36}{45}
{13}{24}{56}
{13}{25}{46}
{13}{26}{45}
{14}{23}{56}
{14}{25}{36}
{14}{26}{35}
{15}{23}{46}
{15}{24}{36}
{15}{26}{34}
{16}{23}{45}
{16}{24}{35}
{16}{25}{34}
{1}{2}{3}{4}{5}{6}
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[Length[Select[mps[Join@@Table[Range[n/d], {d}]], SameQ@@Length/@#&]], {n, 10}, {d, Divisors[n]}]
CROSSREFS
KEYWORD
AUTHOR
Gus Wiseman, Dec 26 2018
EXTENSIONS
More terms from Alois P. Heinz, Jan 30 2019
Terms a(38) and beyond from Andrew Howroyd, Feb 03 2022
STATUS
approved