A006927 Number of connected trivalent graphs with 2n nodes and girth exactly 7. (Formerly M3086)

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 21, 545, 30368, 1782839, 95079080, 4686063107

Offset

0,14

References

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..19.

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

Formula

a(n) = A014375(n) - A014376(n).

Crossrefs

Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), this sequence (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: A285380 A139224 A032469 * A014375 A135748 A145386

Adjacent sequences: A006924 A006925 A006926 * A006928 A006929 A006930

Keyword

nonn,hard,more

Author

N. J. A. Sloane.

Extensions

Definition amended to include "connected" (no disconnected yet), and "girth at least 7" minus "girth at least 8" formula provided by Jason Kimberley, Dec 12 2009

Status

approved