A185043 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 377, 2026, 13349, 104593, 930571, 9124627, 96699740, 1095467916, 13175254799, 167460501260, 2241576473025, 31510509517563, 464047467911837, 7143984462730072, 114749034352969037, 1919656978492976231

Offset

0,13

Links

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

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

Formula

a(n) = A033483(n) - A185244(n).

Crossrefs

4-regular simple graphs with girth exactly 3: A184943 (connected), this sequence (disconnected), A185143 (not necessarily connected).

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), this sequence (k=4), A185053 (k=5), A185063 (k=6).

Disconnected 4-regular simple graphs with girth exactly g: this sequence (g=3), A185044 (g=4).

Sequence in context: A148800 A244278 A190343 * A033483 A130522 A006219

Adjacent sequences: A185040 A185041 A185042 * A185044 A185045 A185046

Keyword

nonn,hard

Author

Jason Kimberley, Feb 29 2012

Extensions

Terms a(27)-a(31), due to the extension of A006820 by Andrew Howroyd, from Jason Kimberley, Mar 16 2020

Status

approved