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

0,15

Links

Table of n, a(n) for n=0..37.

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.

Formula

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

Example

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

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).

Sequence in context: A368777 A113766 A204992 * A205405 A112623 A130675

Adjacent sequences: A186723 A186724 A186725 * A186727 A186728 A186729

Keyword

nonn,more,hard

Author

Jason Kimberley, Nov 23 2011

Extensions

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

Status

approved