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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 (list; graph; refs; listen; history; text; internal format)
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 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976.

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth exactly g

FORMULA

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

CROSSREFS

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).

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).

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

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Last modified March 20 23:22 EDT 2019. Contains 321354 sequences. (Running on oeis4.)