A185163 Number of not necessarily connected 6-regular simple graphs on n vertices with girth exactly 3.

0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 21, 266, 7848, 367860, 21609300, 1470293675, 113314233804, 9799685588955, 945095823831066, 101114579937192452, 11945375659139520680, 1551593789610461996972, 220716215902779230578693

Offset

0,10

Links

Table of n, a(n) for n=0..22.

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

Formula

a(n) = A165627(n) - A185364(n).

a(n) = A184963(n) + A185063(n). - Falk Hüffner, May 21 2026

Crossrefs

Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), A185643 (triangle); fixed k: A026796 (k=2), A185133 (k=3), A185143 (k=4), A185153 (k=5), this sequence (k=6).

Sequence in context: A198004 A184960 A184963 * A184961 A006822 A165627

Adjacent sequences: A185160 A185161 A185162 * A185164 A185165 A185166

Keyword

nonn,hard,more

Author

Jason Kimberley, Mar 21 2012

Extensions

a(18)-a(22) from Falk Hüffner, May 21 2026

Status

approved