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A005176 Number of regular graphs with n unlabeled nodes.
(Formerly M0303)
40
1, 1, 2, 2, 4, 3, 8, 6, 22, 26, 176, 546, 19002, 389454, 50314870, 2942198546, 1698517037030, 442786966117636, 649978211591622812, 429712868499646587714, 2886054228478618215888598, 8835589045148342277802657274, 152929279364927228928025482936226, 1207932509391069805495173417972533120, 99162609848561525198669168653641835566774 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

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=0..24.

E. Friedman, Illustration of small graphs

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

Jennifer M. Larson, Cheating Because They Can: Social Networks and Norm Violators, 2014. See Footnote 11.

Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

Eric Weisstein's World of Mathematics, Regular Graph.

FORMULA

a(n) = A005177(n) + A068932(n). - David Wasserman, Mar 08 2002

Row sums of triangle A051031.

CROSSREFS

Not necessarily connected simple regular graphs: A005176 (any degree), A051031 (triangular array), specified degree k: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7), A180260 (k=8).

Simple regular graphs of any degree: A005177 (connected), A068932 (disconnected), this sequence (not necessarily connected).

Not necessarily connected regular simple graphs with girth at least g: this sequence (g=3), A185314 (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).

Cf. A295193.

Sequence in context: A133806 A283717 A185333 * A050335 A223537 A140860

Adjacent sequences:  A005173 A005174 A005175 * A005177 A005178 A005179

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David Wasserman, Mar 08 2002

a(15) and a(16) from Jason Kimberley, Sep 25 2009

Edited by Jason Kimberley, Jan 06 2011 and May 24 2012

a(17)-a(21) from Andrew Howroyd, Mar 08 2020

a(22)-a(24) from Andrew Howroyd, Apr 05 2020

STATUS

approved

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Last modified December 2 16:31 EST 2020. Contains 338877 sequences. (Running on oeis4.)