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A165656 Number of disconnected 6-regular (sextic) graphs on n vertices.

%I A165656 #24 Feb 16 2025 08:33:11
%S A165656 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,25,297,8199,377004,22014143,
%T A165656 1493574756,114880777582,9919463450855,955388277929620,
%U A165656 102101882472479938,12050526046888229845,1563967741064673811531,222318116370232302781485,34486536277291555593662301,5817920265098158804699762770
%N A165656 Number of disconnected 6-regular (sextic) graphs on n vertices.
%H A165656 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A165656 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/A068933">Disconnected regular graphs (with girth at least 3)</a>
%H A165656 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/D_k-reg_girth_ge_g_index">Index of sequences counting disconnected k-regular simple graphs with girth at least g</a>
%H A165656 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DisconnectedGraph.html">Disconnected Graph</a>
%H A165656 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularGraph.html">Regular Graph</a>
%H A165656 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SexticGraph.html">Sextic Graph</a>
%F A165656 a = A165627 - A006822 = Euler_transformation(A006822) - A006822.
%F A165656 a(n) = D(n, 6) in the triangle A068933.
%Y A165656 6-regular simple graphs: A006822 (connected), this sequence (disconnected), A165627 (not necessarily connected).
%Y A165656 Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), A033483 (k=4), A165655 (k=5), this sequence (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).
%K A165656 nonn,hard
%O A165656 0,17
%A A165656 _Jason Kimberley_, Sep 28 2009
%E A165656 Terms a(25) and beyond from _Andrew Howroyd_, May 20 2020