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 A006822 Number of connected regular graphs of degree 6 with n nodes. (Formerly M3579) 20
 1, 0, 0, 0, 0, 0, 0, 1, 1, 4, 21, 266, 7849, 367860, 21609300, 1470293675, 113314233808, 9799685588936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 REFERENCES CRC Handbook of Combinatorial Designs, 1996, p. 648. I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS M. Meringer, Tables of Regular Graphs Eric Weisstein's World of Mathematics, Connected Graph Eric Weisstein's World of Mathematics, Regular Graph Eric Weisstein's World of Mathematics, Sextic Graph FORMULA a(n) = A184963(n) + A058276(n). a(n) = A165627(n) - A165656(n). This sequence is the inverse Euler transformation of A165627. CROSSREFS Contribution (almost all) from Jason Kimberley, Feb 10 2011: (Start) 6-regular simple graphs: this sequence (connected), A165656 (disconnected), A165627 (not necessarily connected). Connected regular graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), this sequence (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11). Connected 6-regular simple graphs with girth at least g: this sequence (g=3), A058276 (g=4). Connected 6-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4). (End) Sequence in context: A184963 A185163 A184961 * A165627 A198050 A270482 Adjacent sequences:  A006819 A006820 A006821 * A006823 A006824 A006825 KEYWORD nonn,nice,hard,more AUTHOR EXTENSIONS a(16) and a(17) appended, from running M. Meringer's GENREG at U. Newcastle for 41 processor days and 3.5 processor years, by Jason Kimberley, Sep 04 2009 and Nov 13 2009. STATUS approved

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Last modified November 16 12:40 EST 2018. Contains 317272 sequences. (Running on oeis4.)