

A185114


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


19



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
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OFFSET

0


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 kregular simple graphs with girth at least g


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


EXAMPLE

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


MATHEMATICA

a[n_] := Switch[n, 0, 1, 123, 0, _, 1];
a /@ Range[0, 101] (* JeanFrançois Alcover, Dec 05 2019 *)


CROSSREFS

2regular simple graphs with girth at least 4: this sequence (connected), A185224 (disconnected), A008484 (not necessarily connected).
Connected kregular 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 2regular 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 2regular 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 A224877
Adjacent sequences: A185111 A185112 A185113 * A185115 A185116 A185117


KEYWORD

nonn,easy,changed


AUTHOR

Jason Kimberley, Jan 27 2011


STATUS

approved



