A185114 Number of connected 2-regular simple graphs on n vertices with girth at least 4.

1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0

Comments

Decimal expansion of 9001/90000. - Elmo R. Oliveira, May 05 2024

Links

Table of n, a(n) for n=0..101.

Jason Kimberley, Connected regular graphs with girth at least 4

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

a(0)=1; for 0 < n < 4 a(n)=0; for n >= 4, a(n)=1.

Inverse Euler transformation of A008484.

a(n) = A130543(n) + A000007(n). - Bruno Berselli, Jan 31 2011

G.f.: (x^4-x+1)/(1-x). - Elmo R. Oliveira, May 05 2024

Example

The null graph is vacuously 2-regular and, being acyclic, has infinite girth.
There are no 2-regular simple graphs with 1 or 2 vertices.
The n-cycle has girth n.

Mathematica

a[n_] := Switch[n, 0, 1, 1|2|3, 0, _, 1];
a /@ Range[0, 101] (* Jean-François Alcover, Dec 05 2019 *)

Crossrefs

2-regular simple graphs with girth at least 4: this sequence (connected), A185224 (disconnected), A008484 (not necessarily connected).

Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: this sequence (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).

Connected 2-regular simple graphs with girth at least g: A179184 (g=3), this sequence (g=4), A185115 (g=5), A185116 (g=6), A185117 (g=7), A185118 (g=8), A185119 (g=9).

Connected 2-regular simple graphs with girth exactly g: A185013 (g=3), A185014 (g=4), A185015 (g=5), A185016 (g=6), A185017 (g=7), A185018 (g=8).

Sequence in context: A138711 A285617 A246500 * A154281 A154282 A359552

Adjacent sequences: A185111 A185112 A185113 * A185115 A185116 A185117

Keyword

nonn,easy

Author

Jason Kimberley, Jan 27 2011

Status

approved