

A005177


Number of connected regular graphs with n nodes.
(Formerly M0347)


24



1, 1, 1, 1, 2, 2, 5, 4, 17, 22, 167, 539, 18979, 389436, 50314796, 2942198440, 1698517036411
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OFFSET

0,5


REFERENCES

M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137146. [From Jason Kimberley, Sep 23 2009]
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. Steinbach, Field Guide to Simple Graphs. Design Lab, Albuquerque NM, 1990.


LINKS

Table of n, a(n) for n=0..16.
E. Friedman, Illustration of small graphs
Jason Kimberley, Index of sequences counting connected kregular simple graphs with girth at least g
Markus Meringer, GENREG: A program for Connected Regular Graphs [From Giovanni Resta, Feb 05 2009]
Eric Weisstein's World of Mathematics, Regular Graph.


FORMULA

a(n) = sum of the nth row of A068934.
a(n) = A165647(n)  A165648(n).
This sequence is the inverse Euler transformation of A165647.


CROSSREFS

Regular simple graphs of any degree: this sequence (connected), A068932 (disconnected), A005176 (not necessarily connected).
Connected regular graphs of any degree with girth at least g: this sequence (g=3), A186724 (g=4), A186725 (g=5), A186726 (g=6), A186727 (g=7), A186728 (g=8), A186729 (g=9).
Connected regular simple graphs: this sequence (any degree), A068934 (triangular array); specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).  Jason Kimberley, Nov 03 2011
Sequence in context: A238834 A054079 A210713 * A253600 A045537 A243941
Adjacent sequences: A005174 A005175 A005176 * A005178 A005179 A005180


KEYWORD

nonn,nice,hard,more


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from David Wasserman, Mar 08 2002
a(15) from Giovanni Resta, Feb 05 2009
Terms are sums of the output from M. Meringer's genreg software. To complete a(16) it was run by Jason Kimberley, Sep 23 2009
a(0)=1 (due to the empty graph being vacuously connected and regular) inserted by Jason Kimberley, Apr 11 2012


STATUS

approved



