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

Author

Jason Kimberley, Feb 29 2012

Keywords

• nonn
• hard

Links

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

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).

Formula

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

Extensions

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