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

0,8

Links

Table of n, a(n) for n=0..11.

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 A058275.

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

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 *)

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).

Sequence in context: A293459 A058275 A184954 * A222893 A009712 A128793

Adjacent sequences: A185351 A185352 A185353 * A185355 A185356 A185357

Keyword

hard,nonn,more

Author

Jason Kimberley, Nov 04 2011

Status

approved