A006923 Number of connected trivalent graphs with 2n nodes and with girth exactly 3.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

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

• 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.

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).

Formula

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

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