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A185118 Number of connected 2-regular simple graphs on n vertices with girth at least 8. 11
1, 0, 0, 0, 0, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

LINKS

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

Jason Kimberley, Connected regular graphs with girth at least 8

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

FORMULA

a(0)=1; for 0<n<8 a(n)=0; for n>=8 , a(n)=1.

This sequence is the inverse Euler transformation of A185328.

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.

CROSSREFS

2-regular simple graphs with girth at least 8: this sequence (connected), A185228 (disconnected), A185328 (not necessarily connected).

Connected k-regular simple graphs with girth at least 8: A186728 (any k), A186718 (triangle); specific k: this sequence (k=2), A014376 (k=3).

Connected 2-regular simple graphs with girth at least g: A179184 (g=3), A185114 (g=4), A185115 (g=5), A185116 (g=6), A185117 (g=7), this sequence (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: A287457 A324917 A285898 * A240332 A156297 A015626

Adjacent sequences:  A185115 A185116 A185117 * A185119 A185120 A185121

KEYWORD

nonn,easy

AUTHOR

Jason Kimberley, Jan 28 2011

STATUS

approved

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Last modified April 25 21:06 EDT 2019. Contains 322461 sequences. (Running on oeis4.)