OFFSET
0,4
COMMENTS
A hypertree with singletons is a connected set system (finite set of finite nonempty sets) with density -1, where the density of a set system is the sum of sizes of the parts (weight) minus the number of parts minus the number of vertices.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(7) = 23 hypertrees:
{{1}} {{1,2}} {{1,2,3}} {{1,2,3,4}} {{1,2,3,4,5}}
{{2},{1,2}} {{1,3},{2,3}} {{1,4},{2,3,4}}
{{3},{1,2,3}} {{4},{1,2,3,4}}
{{1},{2},{1,2}} {{2},{1,3},{2,3}}
{{2},{3},{1,2,3}}
{{3},{1,3},{2,3}}
.
{{1,2,3,4,5,6}} {{1,2,3,4,5,6,7}}
{{1,2,5},{3,4,5}} {{1,2,6},{3,4,5,6}}
{{1,5},{2,3,4,5}} {{1,6},{2,3,4,5,6}}
{{5},{1,2,3,4,5}} {{6},{1,2,3,4,5,6}}
{{1},{1,4},{2,3,4}} {{1},{1,5},{2,3,4,5}}
{{1,3},{2,4},{3,4}} {{1,2},{2,5},{3,4,5}}
{{1,4},{2,4},{3,4}} {{1,4},{2,5},{3,4,5}}
{{3},{1,4},{2,3,4}} {{1,5},{2,5},{3,4,5}}
{{3},{4},{1,2,3,4}} {{4},{1,2,5},{3,4,5}}
{{4},{1,4},{2,3,4}} {{4},{1,5},{2,3,4,5}}
{{1},{2},{1,3},{2,3}} {{4},{5},{1,2,3,4,5}}
{{1},{2},{3},{1,2,3}} {{5},{1,2,5},{3,4,5}}
{{2},{3},{1,3},{2,3}} {{5},{1,5},{2,3,4,5}}
{{1},{3},{1,4},{2,3,4}}
{{1},{4},{1,4},{2,3,4}}
{{2},{1,3},{2,4},{3,4}}
{{2},{3},{1,4},{2,3,4}}
{{2},{3},{4},{1,2,3,4}}
{{3},{1,4},{2,4},{3,4}}
{{3},{4},{1,4},{2,3,4}}
{{4},{1,3},{2,4},{3,4}}
{{4},{1,4},{2,4},{3,4}}
{{1},{2},{3},{1,3},{2,3}}
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Oct 31 2018
STATUS
approved