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A006923 Number of connected trivalent graphs with 2n nodes and with girth exactly 3.
(Formerly M2944)
18

%I M2944

%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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Last modified April 24 22:18 EDT 2019. Contains 322446 sequences. (Running on oeis4.)