A006926 - OEIS

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A006926

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

0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7573, 181224, 4624480, 122089998, 3328899586, 93988909755

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,10

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..17.

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

FORMULA

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

CROSSREFS

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).

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).

Sequence in context: A093448 A094653 A135250 * A185136 A014374 A185336

Adjacent sequences: A006923 A006924 A006925 * A006927 A006928 A006929

KEYWORD

nonn,hard,more

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Definition corrected to include "connected", and "girth at least 6" minus "girth at least 7" formula provided by Jason Kimberley, Dec 12 2009

STATUS

approved