A000080 Number of nonisomorphic minimal triangle graphs. (Formerly M1173 N0450)

1, 1, 2, 4, 9, 19, 48, 117, 307, 821, 2277, 6437, 18634, 54775, 163703, 495529, 1518706, 4703848, 14714754, 46444979, 147832051, 474229588, 1532565644

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

Table of n, a(n) for n=3..25.

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

Cf. A048781.

Sequence in context: A052328 A133228 A036717 * A327017 A153447 A076893

Adjacent sequences: A000077 A000078 A000079 * A000081 A000082 A000083

Keyword

nonn,more,nice

Author

N. J. A. Sloane

Extensions

Three more terms from Arlin Anderson (starship1(AT)gmail.com)

a(17)-a(25) from Martin Fuller, Mar 23 2015

Status

approved