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Number of not necessarily connected 4-regular simple graphs on n vertices with girth exactly 3.
10

%I #23 Mar 17 2020 12:11:46

%S 0,0,0,0,0,1,1,2,5,16,58,264,1535,10755,87973,803973,8020967,86029760,

%T 983431053,11913921910,152352965278,2050065073002,28951233955602,

%U 428086557232387

%N Number of not necessarily connected 4-regular simple graphs on n vertices with girth exactly 3.

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_k-reg_girth_eq_g_index">Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g</a>

%F a(n) = A033301(n) - A185344(n).

%F a(n) = A184943(n) + A185043(n).

%Y 4-regular simple graphs with girth exactly 3: A184943 (connected), A185043 (disconnected), this sequence (not necessarily connected).

%Y Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), A185643 (triangle); fixed k: A026796 (k=2), A185133 (k=3), this sequence (k=4), A185153 (k=5), A185163 (k=6).

%Y Not necessarily connected 4-regular simple graphs with girth exactly g: A185140 (triangle); fixed g: this sequence (g=3), A185144 (g=4).

%K nonn,hard,more

%O 0,8

%A _Jason Kimberley_, Mar 12 2012

%E a(22) corrected and a(23) appended, due to the correction and extension of A033301 by _Andrew Howroyd_, from _Jason Kimberley_, Mar 14 2020