A185118 Number of connected 2-regular simple graphs on n vertices with girth at least 8.

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

Offset

0

Comments

Decimal expansion of 90000001/900000000. - Elmo R. Oliveira, May 29 2024

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.

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

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.

G.f.: (x^8-x+1)/(1-x). - Elmo R. Oliveira, May 29 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.

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: A369001 A361024 A354037 * A240332 A156297 A373483

Adjacent sequences: A185115 A185116 A185117 * A185119 A185120 A185121

Keyword

nonn,easy

Author

Jason Kimberley, Jan 28 2011

Status

approved