A185119 Number of connected 2-regular simple graphs on n vertices with girth at least 9.

1, 0, 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

Offset

0

Comments

Decimal expansion of 900000001/9000000000. - Elmo R. Oliveira, May 29 2024

Links

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

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 < 9 a(n)=0; for n >= 9, a(n)=1.

Inverse Euler transformation of A185329.

G.f.: (x^9-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 9: this sequence (connected), A185229 (disconnected), A185329 (not necessarily connected).

Connected k-regular simple graphs with girth at least 9: A186729 (all k), A186719 (triangular array), this sequence (k=2).

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), 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: A015494 A267142 A373838 * A280130 A304002 A126811

Adjacent sequences: A185116 A185117 A185118 * A185120 A185121 A185122

Keyword

nonn,easy

Author

Jason Kimberley, Jan 28 2011

Status

approved