OFFSET
0
COMMENTS
Decimal expansion of 90001/900000. - Elmo R. Oliveira, May 28 2024
LINKS
FORMULA
a(0)=1; for 0 < n < 5 a(n)=0; for n >= 5, a(n)=1.
This sequence is the inverse Euler transformation of A185325.
G.f.: (x^5-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}, 100, 1] (* Paolo Xausa, Aug 02 2024 *)
CROSSREFS
2-regular simple graphs with girth at least 5: this sequence (connected), A185225 (disconnected), A185325 (not necessarily connected).
Connected k-regular simple graphs with girth at least 5: A186725 (all k), A186715 (triangle); this sequence (k=2), A014372 (k=3), A058343 (k=4), A205295 (k=5).
Connected 2-regular simple graphs with girth at least g: A179184 (g=3), A185114 (g=4), this sequence (g=5), A185116 (g=6), A185117 (g=7), A185118 (g=8), A185119 (g=9).
KEYWORD
nonn,easy
AUTHOR
Jason Kimberley, Jan 28 2011
STATUS
approved