A006924 Number of connected trivalent graphs with 2n nodes and girth exactly 4. (Formerly M1526)

0, 0, 0, 1, 2, 5, 20, 101, 743, 7350, 91763, 1344782, 22160335, 401278984, 7885687604, 166870266608, 3781101495300

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) = A014371(n) - A014372(n).

Crossrefs

Connected k-regular simple graphs with girth exactly 4: this sequence (k=3), A184944 (k=4), A184954 (k=5), A184964 (k=6), A184974 (k=7).

Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), this sequence (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: A039909 A009551 A323274 * A212580 A370669 A261779

Adjacent sequences: A006921 A006922 A006923 * A006925 A006926 A006927

Keyword

nonn,hard,more

Author

N. J. A. Sloane.

Extensions

Definition corrected to include "connected", and "girth at least 4" minus "girth at least 5" formula provided by Jason Kimberley, Dec 12 2009

Status

approved