OFFSET
3,3
COMMENTS
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
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. Bowen, The generation of minimal triangle graphs, Math. Comp. 21 (1967), 248-250.
Martin Fuller, C program
N. J. A. Sloane, Illustration of initial terms (annotated version of figure from Bowen 1967).
EXAMPLE
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
CROSSREFS
KEYWORD
nonn,more,nice
AUTHOR
EXTENSIONS
Three more terms from Arlin Anderson (starship1(AT)gmail.com)
a(17)-a(25) from Martin Fuller, Mar 23 2015
STATUS
approved