OFFSET
1,4
COMMENTS
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 counted under a(9).
The a(1) = 0 through a(6) = 11 subsets:
. . {1,2,3} {1,3,4} {1,4,5} {1,5,6}
{1,2,3,4} {2,3,5} {2,4,6}
{1,2,4,5} {1,2,3,6}
{2,3,4,5} {1,2,5,6}
{1,2,3,4,5} {1,3,4,6}
{2,3,5,6}
{3,4,5,6}
{1,2,3,4,6}
{1,2,4,5,6}
{2,3,4,5,6}
{1,2,3,4,5,6}
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