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

Offset: 0

Author

Jason Kimberley, Nov 03 2011

Keywords

• nonn
• hard
• more

Links

• 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

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).

Programs

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 *)

Formula

This sequence is the Euler transformation of A033886.

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