A185354 Number of not necessarily connected 5-regular simple graphs on 2n vertices with girth at least 4.

1, 0, 0, 0, 0, 1, 1, 7, 388, 406824, 1125022326, 3813549359275

Offset: 0

Author

Jason Kimberley, Nov 04 2011

Keywords

• hard
• nonn
• 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

5-regular simple graphs on 2n vertices with girth at least 4: A058275 (connected), A185254 (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), A185344 (k=4), this sequence (k=5), A185364 (k=6).

Programs

Mathematica

A058275 = Cases[Import["https://oeis.org/A058275/b058275.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A058275]  (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

Formula

This sequence is the Euler transformation of A058275.

a(n) = A058275(n) + A185254(n).