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%I M2944 #28 Sep 28 2023 02:05:22
%S 0,0,1,1,3,13,63,399,3268,33496,412943,5883727,94159721,1661723296,
%T 31954666517,663988090257,14814445040728
%N Number of connected trivalent graphs with 2n nodes and with girth exactly 3.
%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 F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, <a href="http://alexandria.tue.nl/repository/books/252909.pdf">Computer investigations of cubic graphs</a>, T.H.-Report 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976.
%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) = A002851(n) - A014371(n).
%Y Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: this sequence (g=3), A006924 (g=4), A006925 (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 0,5
%A _N. J. A. Sloane_
%E Definition corrected to include "connected", and "girth at least 3" minus "girth at least 4" formula provided by _Jason Kimberley_, Dec 12 2009
%E Terms a(14), a(15), and a(16) appended using "new" terms of A014371 by _Jason Kimberley_, Nov 16 2011
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