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

0,19

Links

Table of n, a(n) for n=0..31.

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

Formula

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

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

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).

Sequence in context: A325912 A365086 A185044 * A329920 A006929 A216613

Adjacent sequences: A185241 A185242 A185243 * A185245 A185246 A185247

Keyword

nonn,more,hard

Author

Jason Kimberley, Feb 22 2011

Extensions

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

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

Status

approved