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URL: https://oeis.org/A184944

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A184944
Number of connected 4-regular simple graphs on n vertices with girth exactly 4.
15
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
0,11
FORMULA
a(n) = A033886(n) - A058343(n).
EXAMPLE
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}.
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).
Sequence in context: A199127 A093044 A151366 * A033886 A185144 A185344
KEYWORD
nonn,hard,more
AUTHOR
Jason Kimberley, Jan 26 2011
EXTENSIONS
a(23) was appended by the author once A033886(23) was known, Nov 03 2011
STATUS
approved