A185254 -id:A185254 - cp's OEIS frontend

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

Jason Kimberley, Nov 04 2011

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

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).

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 *)

This sequence is the Euler transformation of A058275.

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

A185053 Number of disconnected 5-regular simple graphs on 2n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 3, 66, 8029, 3484759, 2595985769, 2815099031409

Offset: 0

Jason Kimberley, Mar 10 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), this sequence (k=5), A185063 (k=6).

a(n) = A165655(n) - A185254(n).

cp's OEIS Frontend

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

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