%I #40 May 20 2020 03:01:34

%S 1,0,0,0,0,0,0,0,0,0,0,1,1,10,540,805579,2585136741,9799685588961,

%T 42700033549946255,214755319657939505396,1251392240942040452186675,

%U 8462215143144463851848329660,66398444413512642732641312352087,603696608755863722277922645973602843,6346188247029220928621633703157327186101

%N Number of connected regular graphs of degree 10 with n nodes.

%C Since the nontrivial 10-regular graph with the least number of vertices is K_11, there are no disconnected 10-regular graphs with less than 22 vertices. Thus for n<22 this sequence also gives the number of all 10-regular graphs on n vertices. - _Jason Kimberley_, Sep 25 2009

%D CRC Handbook of Combinatorial Designs, 1996, p. 648.

%D 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.

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_ge_g_index">Index of sequences counting connected k-regular simple graphs with girth at least g</a>

%H M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>

%H M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/pdf/pub/FastGenRegGraphJGT.pdf">Fast Generation of Regular Graphs and Construction of Cages</a>, Journal of Graph Theory, 30 (1999), 137-146.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RegularGraph.html">Regular Graph.</a>

%e The null graph on 0 vertices is vacuously connected and 10-regular; since it is acyclic, it has infinite girth. - _Jason Kimberley_, Feb 10 2011

%Y 10-regular simple graphs: this sequence (connected), A185203 (disconnected).

%Y 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), A014378 (k=8), A014381 (k=9), this sequence (k=10), A014384 (k=11).

%K nonn,hard

%O 0,14

%A _N. J. A. Sloane_

%E Using the symmetry of A051031, a(16) and a(17) from _Jason Kimberley_, Sep 25 2009 and Jan 03 2011

%E a(18)-a(21) from _Andrew Howroyd_, Mar 13 2020

%E a(22)-a(24) from _Andrew Howroyd_, May 19 2020