A186726 Number of connected regular graphs with n nodes and girth at least 6.

1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 6, 1, 33, 1, 386, 1, 7575, 1, 181229, 1, 4624503, 1, 122090549, 1, 3328929974, 1, 93990693868, 26, 2754223099408, 13505

Offset: 0

Author

Jason Kimberley, Nov 23 2011

Keywords

• nonn
• more
• hard

Examples

			a(37) = 0 + 0 + 1 + 0 + 13504 = 13505.
		

Links

• Jason Kimberley, Connected regular graphs with girth at least 6
• 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.

Crossrefs

Connected regular graphs of any degree with girth at least g: A005177 (g=3), A186724 (g=4), A186725 (g=5), this sequence (g=6), A186727 (g=7), A186728 (g=8), A186729 (g=9).

Connected k-regular simple graphs with girth at least 6: this sequence (any k), A186716 (triangle); specific k: A185116 (k=2), A014374 (k=3), A058348 (k=4).

Formula

a(n) = sum of the n-th row of A186716.

Extensions

a(36)-a(37) from Jinyuan Wang, Mar 02 2020