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A185344 Number of not necessarily connected 4-regular simple graphs on n vertices with girth at least 4. 9
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

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Last modified September 29 12:15 EDT 2020. Contains 337431 sequences. (Running on oeis4.)