OFFSET
1,2
EXAMPLE
The set s = {3,4,6,8,9} has set partitions {{3,4,6,8,9}} and {{3,4,8},{6,9}} with equal block-sums, so s is not counted under a(9).
The a(1) = 1 through a(5) = 11 subsets:
{1} {2} {3} {4} {5}
{1,2} {1,3} {1,4} {1,5}
{2,3} {2,4} {2,5}
{3,4} {3,5}
{1,2,4} {4,5}
{2,3,4} {1,2,5}
{1,3,5}
{2,4,5}
{3,4,5}
{1,2,3,5}
{1,3,4,5}
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]& /@ sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&Length[Select[sps[#], SameQ@@Total/@#&]]==1&]], {n, 10}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Apr 17 2024
STATUS
approved