A185335 Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 5.

1, 0, 0, 0, 0, 1, 2, 9, 49, 455, 5784, 90940, 1620491, 31478651, 656784488, 14621878339, 345975756388

Offset

0,7

Links

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

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

Formula

This sequence is the Euler transformation of A014372.

Mathematica

A014372 = Cases[Import["https://oeis.org/A014372/b014372.txt", "Table"], {_, _}][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A014372] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

Crossrefs

3-regular simple graphs with girth at least 5: A014372 (connected), A185235 (disconnected), this sequence (not necessarily connected).

Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), A185334 (g=4), this sequence (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).

Not necessarily connected k-regular simple graphs with girth at least 5: A185315 (any k), A185305 (triangle); specified degree k: A185325 (k=2), this sequence (k=3).

Sequence in context: A357294 A109323 A014372 * A262752 A138416 A328741

Adjacent sequences: A185332 A185333 A185334 * A185336 A185337 A185338

Keyword

nonn,more,hard

Author

Jason Kimberley, Jan 28, 2011

Status

approved