%I M1173 N0450
%S 1,1,2,4,9,19,48,117,307,821,2277,6437,18634,54775,163703,495529,
%T 1518706,4703848,14714754,46444979,147832051,474229588,1532565644
%N Number of nonisomorphic minimal triangle graphs.
%C Let T be a set of triples (sets of three distinct points) from a set of n points. The graph G(T) has a vertex for each point, with two vertices joined by an edge if the two points belong to one of the triples. Then a(n) is the number of ways to choose T so that G(T) is connected and minimal, meaning that it becomes disconnected if any triple is omitted.  _N. J. A. Sloane_, Jan 22 2014
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. Bowen, <a href="http://dx.doi.org/10.1090/S00255718196702232761">The generation of minimal triangle graphs</a>, Math. Comp. 21 (1967), 248250.
%H Martin Fuller, <a href="/A000080/a000080.c.txt">C program</a>
%H N. J. A. Sloane, <a href="/A000080/a000080.jpg">Illustration of initial terms</a> (annotated version of figure from Bowen 1967).
%e The triples on n = 3 through 6 points are (see "Illustration" link): 3 : ABC; 4 : ABC, ABD; 5 : ABC, ADE; and ABC, ABD, ABE, 6 : ABD, BCD, DEF; ABC, BCD, DEF; ABF, BCD, DEF; ABC, ABD, ABE, ABF.  _N. J. A. Sloane_, Jan 22 2014
%Y Cf. A048781.
%K nonn,more,nice
%O 3,3
%A _N. J. A. Sloane_
%E Three more terms from Arlin Anderson (starship1(AT)gmail.com)
%E a(17)a(25) from _Martin Fuller_, Mar 23 2015
