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

Author

Jason Kimberley, Oct 17 2011

Keywords

• nonn
• hard
• more

Links

• 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]

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).

Formula

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

Extensions

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