

A006923


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


18



0, 0, 1, 1, 3, 13, 63, 399, 3268, 33496, 412943, 5883727, 94159721, 1661723296, 31954666517, 663988090257, 14814445040728
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OFFSET

0,5


REFERENCES

CRC Handbook of Combinatorial Designs, 1996, p. 647.
Gordon Royle, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=0..16.
F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, Computer investigations of cubic graphs, T.H.Report 76WSK01, Technological University Eindhoven, Dept. Mathematics, 1976.
Jason Kimberley, Index of sequences counting connected kregular simple graphs with girth exactly g


FORMULA

a(n) = A002851(n)  A014371(n).


CROSSREFS

Connected 3regular 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).
Connected 3regular 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).
Sequence in context: A202837 A180111 A292183 * A283667 A011272 A200719
Adjacent sequences: A006920 A006921 A006922 * A006924 A006925 A006926


KEYWORD

nonn,hard,more


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Definition corrected to include "connected", and "girth at least 3" minus "girth at least 4" formula provided by Jason Kimberley, Dec 12 2009
Terms a(14), a(15), and a(16) appended using "new" terms of A014371 by Jason Kimberley, Nov 16 2011


STATUS

approved



