OFFSET
1,3
COMMENTS
a(n) grows asymptotically faster than sqrt(n)*exp(2*Pi*sqrt(n/log(n))/sqrt(3)).
LINKS
Jernej Azarija, Counting graphs with different numbers of spanning trees through the counting of prime partitions (preprint, 2012).
Jernej Azarija, Maximal class of simple graphs of order n with mutually distinct number of spanning trees, (Mathoverflow).
J. Sedlacek, On the number of spanning trees of finite graphs, Cas. Pro. Pest Mat., Vol. 94 (1969) 217-221.
EXAMPLE
a(3) = 2 since any connected graph on 3 vertices can either have 1 spanning tree (any tree) or 3 (triangle).
PROG
(Sage) # needs the package nauty:
len( set([g.spanning_trees_count() for g in graphs.nauty_geng('-c ' + str(n)) ]))
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jernej Azarija, Jun 27 2012
EXTENSIONS
a(11) from Jernej Azarija, Sep 07 2012
STATUS
approved