A185143 Number of not necessarily connected 4-regular simple graphs on n vertices with girth exactly 3.

0, 0, 0, 0, 0, 1, 1, 2, 5, 16, 58, 264, 1535, 10755, 87973, 803973, 8020967, 86029760, 983431053, 11913921910, 152352965278, 2050065073002, 28951233955602, 428086557232387

Offset

0,8

Links

Table of n, a(n) for n=0..23.

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

Formula

a(n) = A033301(n) - A185344(n).

a(n) = A184943(n) + A185043(n).

Crossrefs

4-regular simple graphs with girth exactly 3: A184943 (connected), A185043 (disconnected), this sequence (not necessarily connected).

Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), A185643 (triangle); fixed k: A026796 (k=2), A185133 (k=3), this sequence (k=4), A185153 (k=5), A185163 (k=6).

Not necessarily connected 4-regular simple graphs with girth exactly g: A185140 (triangle); fixed g: this sequence (g=3), A185144 (g=4).

Sequence in context: A300042 A019448 A243326 * A280760 A350717 A000753

Adjacent sequences: A185140 A185141 A185142 * A185144 A185145 A185146

Keyword

nonn,hard,more

Author

Jason Kimberley, Mar 12 2012

Extensions

a(22) corrected and a(23) appended, due to the correction and extension of A033301 by Andrew Howroyd, from Jason Kimberley, Mar 14 2020

Status

approved