A000717 Number of graphs with n nodes and floor(n(n-1)/4) edges.

1, 1, 1, 3, 6, 24, 148, 1646, 34040, 1358852, 106321628, 16006173014, 4525920859198, 2404130854745735, 2426376196165902704, 4648429222263945620900, 16788801124652327714275292, 114722035311851620271616102401

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

This is the largest number of graphs with n vertices that all have the same number of edges. a(n) <= A371161(n). - Allan Bickle, Apr 18 2024

Examples

			There are three graphs with 4 vertices and 3 edges, K_3 U K_1, K_{1,3}, and P_4, so a(4) = 3. - _Allan Bickle_, Apr 18 2024
		

References

• J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 146.
• 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

• Sean A. Irvine, Table of n, a(n) for n = 1..40
• M. L. Stein and P. R. Stein, Enumeration of Linear Graphs and Connected Linear Graphs up to p = 18 Points. Report LA-3775, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Oct 1967

Crossrefs

Cf. A008406, A371161.

Extensions

More terms from Sean A. Irvine, Mar 10 2011