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%I M1526 #32 May 01 2014 02:40:01
%S 0,0,0,1,2,5,20,101,743,7350,91763,1344782,22160335,401278984,
%T 7885687604,166870266608,3781101495300
%N Number of connected trivalent graphs with 2n nodes and girth exactly 4.
%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) = A014371(n) - A014372(n).
%Y Connected k-regular simple graphs with girth exactly 4: this sequence (k=3), A184944 (k=4), A184954 (k=5), A184964 (k=6), A184974 (k=7).
%Y Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), this sequence (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 4" minus "girth at least 5" formula provided by _Jason Kimberley_, Dec 12 2009
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