A185116 - OEIS

A185116

Number of connected 2-regular simple graphs on n vertices with girth at least 6.

1, 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, 1, 1

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OFFSET

COMMENTS

Decimal expansion of 900001/9000000. - Elmo R. Oliveira, May 28 2024

LINKS

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

Jason Kimberley, Connected regular graphs with girth at least 6.

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 < 6 a(n)=0; for n >= 6, a(n)=1.

This sequence is the inverse Euler transformation of A185326.

G.f.: (x^6-x+1)/(1-x). - Elmo R. Oliveira, May 28 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

PadRight[{1, 0, 0, 0, 0, 0}, 100, 1] (* Paolo Xausa, Aug 02 2024 *)

CROSSREFS

2-regular simple graphs with girth at least 6: this sequence (connected), A185226 (disconnected), A185326 (not necessarily connected).

Connected k-regular simple graphs with girth at least 6: A186726 (any k), A186716 (triangle); specified degree k: this sequence (k=2), A014374 (k=3), A058348 (k=4).

Connected 2-regular simple graphs with girth at least g: A179184 (g=3), A185114 (g=4), A185115 (g=5), this sequence (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: A111412 A080111 A204545 * A014034 A014059 A015934

Adjacent sequences: A185113 A185114 A185115 * A185117 A185118 A185119

KEYWORD

nonn,easy

AUTHOR

Jason Kimberley, Jan 28 2011

STATUS

approved