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A185117
Number of connected 2-regular simple graphs on n vertices with girth at least 7.
13
1, 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, 1
OFFSET
0
COMMENTS
Decimal expansion of 9000001/90000000. - Elmo R. Oliveira, May 29 2024
FORMULA
a(0)=1; for 0 < n < 7 a(n)=0; for n >= 7, a(n)=1.
This sequence is the inverse Euler transformation of A185327.
G.f.: (x^7-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.
MATHEMATICA
PadRight[{1, 0, 0, 0, 0, 0, 0}, 100, 1] (* Paolo Xausa, Jun 30 2024 *)
CROSSREFS
2-regular simple graphs with girth at least 7: this sequence (connected), A185227 (disconnected), A185327 (not necessarily connected).
Connected k-regular simple graphs with girth at least 7: A186727 (any k), A186717 (triangle); specific k: this sequence (k=2), A014375 (k=3).
Connected 2-regular simple graphs with girth at least g: A179184 (g=3), A185114 (g=4), A185115 (g=5), A185116 (g=6), this sequence (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: A374110 A297199 A373477 * A014045 A015269 A016347
KEYWORD
nonn,easy
AUTHOR
Jason Kimberley, Jan 28 2011
STATUS
approved