A185334 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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