A185244 Number of disconnected 4-regular simple graphs on n vertices with girth at least 4.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 15, 35, 247, 1692, 17409, 197924, 2492824, 33117880, 461597957, 6709514218, 101153412903, 1597440868898

Offset: 0

Author

Jason Kimberley, Feb 22 2011

Keywords

• nonn
• more
• hard

Links

• Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Crossrefs

4-regular simple graphs with girth at least 4: A033886 (connected), this sequence (disconnected), A185344 (not necessarily connected).

Disconnected 4-regular simple graphs with girth at least g: A033483 (g=3), this sequence (g=4), A185245 (g=5), A185246 (g=6).

Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), this sequence (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).

Formula

a(n) = A185344(n) - A033886(n) = Euler_transformation(A033886)(n) - A033886(n).

a(n) = A185044(n) + A185245(n).

Extensions

a(31) appended by the author once A033886(23) was known, Nov 03 2011

a(31) corrected by the author, Jan 05 2013