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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS E. Friedman, Illustration of small graphs Daniel R. Herber, Enhancements to the perfect matching approach for graph enumeration-based engineering challenges, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2020). Markus Meringer, GENREG: A program for Connected Regular Graphs M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. [Jason Kimberley, Sep 23 2009] 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) = sum of the n-th 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), 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 Sequence in context: A054079 A210713 A283825 * A253600 A045537 A243941 Adjacent sequences:  A005174 A005175 A005176 * A005178 A005179 A005180 KEYWORD nonn,nice,hard AUTHOR 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 a(17)-a(21) from Andrew Howroyd, Mar 10 2020 a(22)-a(24) from Andrew Howroyd, May 19 2020 STATUS approved

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Last modified April 21 03:18 EDT 2021. Contains 343145 sequences. (Running on oeis4.)