A185344 - OEIS

A185344

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

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 12, 31, 220, 1606, 16829, 193900, 2452820, 32670332, 456028489, 6636066134, 100135577994, 1582718914660

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

OFFSET

0,11

LINKS

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

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

This sequence is the Euler transformation of A033886.

a(n) = A033886(n) + A185244(n).

MATHEMATICA

A033886 = Cases[Import["https://oeis.org/A033886/b033886.txt", "Table"], {_, _}][[All, 2]];

(* EulerTransform is defined in A005195 *)

EulerTransform[Rest @ A033886] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

CROSSREFS

4-regular simple graphs with girth at least 4: A033886 (connected), A185244 (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), A185334 (k=3), this sequence (k=4), A185354 (k=5), A185364 (k=6).

Sequence in context: A184944 A033886 A185144 * A237275 A087131 A199240

Adjacent sequences: A185341 A185342 A185343 * A185345 A185346 A185347

KEYWORD

nonn,hard,more

AUTHOR

Jason Kimberley, Nov 03 2011

STATUS

approved