A185334 Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 4.

1, 0, 0, 1, 2, 6, 23, 112, 801, 7840, 97723, 1436873, 23791155, 432878091, 8544173926, 181519645163, 4127569521160

Offset

0,5

Comments

The null graph on 0 vertices is vacuously 3-regular; since it is acyclic, it has infinite girth.

Links

Table of n, a(n) for n=0..16.

Jason Kimberley, Not necessarily connected k-regular graphs with girth at least 4

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

Formula

Euler transformation of A014371.

Mathematica

A014371 = Cases[Import["https://oeis.org/A014371/b014371.txt", "Table"], {_, _}][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A014371] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

Crossrefs

3-regular simple graphs with girth at least 4: A014371 (connected), A185234 (disconnected), this sequence (not necessarily connected).

Not necessarily connected k-regular simple graphs with girth at least 4: A185314 (any k), A185304 (triangle); specified degree k: A008484 (k=2), this sequence (k=3), A185344 (k=4), A185354 (k=5), A185364 (k=6).

Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), this sequence (g=4), A185335 (g=5), A185336 (g=6).

Not necessarily connected 3-regular simple graphs with girth *exactly* g: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).

Sequence in context: A063255 A117158 A317128 * A290280 A349087 A370508

Adjacent sequences: A185331 A185332 A185333 * A185335 A185336 A185337

Keyword

nonn,more,hard

Author

Jason Kimberley, Feb 15 2011

Status

approved