%I #46 Dec 05 2022 11:01:15

%S 1,0,0,0,1,5,1547,21609301,733351105934,42700033549946250,

%T 4073194598236125132578,613969628444792223002008202,

%U 141515621596238755266884806115631

%N Number of connected regular graphs of degree 7 with 2n nodes.

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

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

%F a(n) = A184973(n) + A181153(n).

%F a(n) = A165628(n) - A165877(n).

%F This sequence is the inverse Euler transformation of A165628.

%e a(0)=1 because the null graph (with no vertices) is vacuously 7-regular and connected.

%Y Contribution (almost all) from _Jason Kimberley_, Feb 10 2011: (Start)

%Y 7-regular simple graphs: this sequence (connected), A165877 (disconnected), A165628 (not necessarily connected).

%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), this sequence (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).

%Y Connected 7-regular simple graphs with girth at least g: this sequence (g=3), A181153 (g=4).

%Y Connected 7-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4), A184965 (g=5). (End)

%K nonn,nice,hard,more

%O 0,6

%A _N. J. A. Sloane_

%E Added another term from Meringer's page. _Dmitry Kamenetsky_, Jul 28 2009

%E Term a(8) (on Meringer's page) was found from running Meringer's GENREG for 325 processor days at U. Newcastle by _Jason Kimberley_, Oct 02 2009

%E a(9)-a(11) from _Andrew Howroyd_, Mar 13 2020

%E a(12) from _Andrew Howroyd_, May 19 2020