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A185116
Number of connected 2-regular simple graphs on n vertices with girth at least 6.
14
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
OFFSET
0
COMMENTS
Decimal expansion of 900001/9000000. - Elmo R. Oliveira, May 28 2024
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
KEYWORD
nonn,easy
AUTHOR
Jason Kimberley, Jan 28 2011
STATUS
approved