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A185119
Number of connected 2-regular simple graphs on n vertices with girth at least 9.
11
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
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
KEYWORD
nonn,easy
AUTHOR
Jason Kimberley, Jan 28 2011
STATUS
approved