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Number of connected trivalent graphs with 2n nodes and girth exactly 6.
(Formerly M3969)
14

%I M3969 #22 May 01 2014 02:40:01

%S 0,0,0,0,0,0,0,1,1,5,32,385,7573,181224,4624480,122089998,3328899586,

%T 93988909755

%N Number of connected trivalent graphs with 2n nodes and girth exactly 6.

%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) = A014374(n) - A014375(n).

%Y Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), A006924 (g=4), A006925 (g=5), this sequence (g=6), A006927 (g=7).

%Y Connected 3-regular simple graphs with girth at least g: A185131 (triangle); A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).

%K nonn,hard,more

%O 0,10

%A _N. J. A. Sloane_.

%E Definition corrected to include "connected", and "girth at least 6" minus "girth at least 7" formula provided by _Jason Kimberley_, Dec 12 2009