A006927 Number of connected trivalent graphs with 2n nodes and girth exactly 7.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

References

• Gordon Royle, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

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).

Formula

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

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