A005177 - OEIS (original) (raw)

A005177

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

30

1, 1, 1, 1, 2, 2, 5, 4, 17, 22, 167, 539, 18979, 389436, 50314796, 2942198440, 1698517036411, 442786966115560, 649978211591600286, 429712868499646474880, 2886054228478618211088773, 8835589045148342277771518309, 152929279364927228928021274993215, 1207932509391069805495173301992815105, 99162609848561525198669168640159162918815

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

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.)

FORMULA

a(n) = sum of the n-th row of A068934.

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), A275420 (multisets).

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

EXTENSIONS

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