A186725 Number of connected regular graphs with n nodes and girth at least 5.

1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 3, 1, 10, 1, 50, 1, 456, 2, 5786, 9, 91070, 3918, 1744339, 4131992, 163639193, 4018022150, 119026595851

Offset

0,11

Links

Table of n, a(n) for n=0..28.

Jason Kimberley, Connected regular graphs with girth at least 5

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

M. Meringer, Tables of Regular Graphs

M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. [Jason Kimberley, Jan 29 2011]

Formula

a(n) = sum of the n-th row of A186715.

Crossrefs

Connected regular graphs of any degree with girth at least g: A005177 (g=3), A186724 (g=4), this sequence (g=5), A186726 (g=6), A186727 (g=7), A186728 (g=8), A186729 (g=9).

Connected k-regular simple graphs with girth at least 5: this sequence (all k), A186715 (triangle); A185115 (k=2), A014372 (k=3), A058343 (k=4), A205295 (k=5).

Sequence in context: A126761 A090559 A088640 * A301935 A237978 A337276

Adjacent sequences: A186722 A186723 A186724 * A186726 A186727 A186728

Keyword

nonn,hard,more

Author

Jason Kimberley, Oct 17 2011

Extensions

a(26) corrected by the author, due to A186715(26,3) being corrected, May 19 2017

Status

approved