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A185335 Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 5. 9

%I #22 Mar 18 2020 09:00:56

%S 1,0,0,0,0,1,2,9,49,455,5784,90940,1620491,31478651,656784488,

%T 14621878339,345975756388

%N Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 5.

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

%F This sequence is the Euler transformation of A014372.

%t A014372 = Cases[Import["https://oeis.org/A014372/b014372.txt", "Table"], {_, _}][[All, 2]];

%t (* EulerTransform is defined in A005195 *)

%t EulerTransform[Rest @ A014372] (* _Jean-François Alcover_, Dec 04 2019, updated Mar 18 2020 *)

%Y 3-regular simple graphs with girth at least 5: A014372 (connected), A185235 (disconnected), this sequence (not necessarily connected).

%Y Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), A185334 (g=4), this sequence (g=5), A185336 (g=6).

%Y Not necessarily connected 3-regular simple graphs with girth *exactly* g: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).

%Y Not necessarily connected k-regular simple graphs with girth at least 5: A185315 (any k), A185305 (triangle); specified degree k: A185325 (k=2), this sequence (k=3).

%K nonn,more,hard

%O 0,7

%A _Jason Kimberley_, Jan 28, 2011

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Last modified March 28 16:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)