A006923 Number of connected trivalent graphs with 2n nodes and with girth exactly 3. (Formerly M2944)

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

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: A370396 A180111 A292183 * A349304 A372507 A283667

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