%I M1879 #21 May 01 2014 02:40:01
%S 0,0,0,0,0,1,2,8,48,450,5751,90553,1612905,31297357,652159389,
%T 14499780660,342646718608
%N Number of connected trivalent graphs with 2n nodes and girth exactly 5.
%D CRC Handbook of Combinatorial Designs, 1996, p. 647.
%D Gordon Royle, personal communication.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_eq_g_index">Index of sequences counting connected k-regular simple graphs with girth exactly g</a>
%F a(n) = A014372(n) - A014374(n).
%Y Connected k-regular simple graphs with girth exactly 5: this sequence (k=3), A184945 (k=4), A184955 (k=5).
%Y Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), A006924 (g=4), this sequence
%Y (g=5), A006926 (g=6), A006927 (g=7).
%Y Connected 3-regular simple graphs with girth at least g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).
%K nonn,hard,more
%O 0,7
%A _N. J. A. Sloane_.
%E Definition corrected to include "connected", and "girth at least 5" minus "girth at least 6" formula provided by _Jason Kimberley_, Dec 12 2009