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 A014378 Number of connected regular graphs of degree 8 with n nodes. 21
 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 94, 10786, 3459386, 1470293676, 733351105935, 423187422492342, 281341168330848873, 214755319657939505395, 187549729101764460261498, 186685399408147545744203815, 210977245260028917322933154987 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS Since the nontrivial 8-regular graph with the least number of vertices is K_9, there are no disconnected 8-regular graphs with less than 18 vertices. Thus for n<18 this sequence is identical to A180260. - Jason Kimberley, Sep 25 2009 and Feb 10 2011 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. LINKS M. Meringer, Tables of Regular Graphs Eric Weisstein's World of Mathematics, Connected Graph Eric Weisstein's World of Mathematics, Octic Graph Eric Weisstein's World of Mathematics, Regular Graph FORMULA a(n) = A184983(n) + A181154(n). a(n) = A180260(n) + A165878(n). This sequence is the inverse Euler transformation of A180260. EXAMPLE a(0)=1 because the null graph (with no vertices) is vacuously 8-regular and connected. CROSSREFS Contribution (almost all) from Jason Kimberley, Feb 10 2011: (Start) 8-regular simple graphs: this sequence (connected), A165878 (disconnected), A180260 (not necessarily connected). Connected regular simple graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), A006822 (k=6), A014377 (k=7), this sequence (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11). Connected 8-regular simple graphs with girth at least g: A184981 (triangle); chosen g: A014378 (g=3), A181154 (g=4). Connected 8-regular simple graphs with girth exactly g: A184980 (triangle); chosen g: A184983 (g=3). (End) Sequence in context: A184983 A184980 A184981 * A180260 A058465 A290984 Adjacent sequences:  A014375 A014376 A014377 * A014379 A014380 A014381 KEYWORD nonn,hard AUTHOR EXTENSIONS Using the symmetry of A051031, a(15) and a(16) were appended by Jason Kimberley, Sep 25 2009 a(17)-a(22) from Andrew Howroyd, Mar 13 2020 STATUS approved

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Last modified July 12 23:28 EDT 2020. Contains 335669 sequences. (Running on oeis4.)