A006925 Number of connected trivalent graphs with 2n nodes and girth exactly 5. (Formerly M1879)

0, 0, 0, 0, 0, 1, 2, 8, 48, 450, 5751, 90553, 1612905, 31297357, 652159389, 14499780660, 342646718608

Offset

0,7

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.

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

Formula

a(n) = A014372(n) - A014374(n).

Crossrefs

Connected k-regular simple graphs with girth exactly 5: this sequence (k=3), A184945 (k=4), A184955 (k=5).

Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), A006924 (g=4), this sequence

(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: A112541 A052667 A327904 * A185135 A238805 A005867

Adjacent sequences: A006922 A006923 A006924 * A006926 A006927 A006928

Keyword

nonn,hard,more

Author

N. J. A. Sloane.

Extensions

Definition corrected to include "connected", and "girth at least 5" minus "girth at least 6" formula provided by Jason Kimberley, Dec 12 2009

Status

approved