A184944 Number of connected 4-regular simple graphs on n vertices with girth exactly 4.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 12, 31, 220, 1606, 16828, 193900, 2452818, 32670329, 456028472, 6636066091, 100135577616, 1582718909051

Offset: 0

Author

Jason Kimberley, Jan 26 2011

Keywords

• nonn
• hard
• more

Examples

			a(0)=0 because even though the null graph (on zero vertices) is vacuously 4-regular and connected, since it is acyclic, it has infinite girth.
The a(8)=1 graph is the complete bipartite graph K_{4,4}.
		

Links

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

Crossrefs

4-regular simple graphs with girth exactly 4: this sequence (connected), A185044 (disconnected), A185144 (not necessarily connected).

Connected k-regular simple graphs with girth exactly 4: A006924 (k=3), this sequence (k=4), A184954 (k=5), A184964 (k=6), A184974 (k=7).

Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).

Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), this sequence (g=4), A184945 (g=5).

Formula

a(n) = A033886(n) - A058343(n).

Extensions

a(23) was appended by the author once A033886(23) was known, Nov 03 2011