# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a185118 Showing 1-1 of 1 %I A185118 #19 Jun 15 2024 18:41:37 %S A185118 1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, %T A185118 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, %U A185118 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 %N A185118 Number of connected 2-regular simple graphs on n vertices with girth at least 8. %C A185118 Decimal expansion of 90000001/900000000. - _Elmo R. Oliveira_, May 29 2024 %H A185118 Jason Kimberley, Connected regular graphs with girth at least 8. %H A185118 Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g. %H A185118 Index entries for linear recurrences with constant coefficients, signature (1). %F A185118 a(0)=1; for 0 < n < 8 a(n)=0; for n >= 8, a(n)=1. %F A185118 This sequence is the inverse Euler transformation of A185328. %F A185118 G.f.: (x^8-x+1)/(1-x). - _Elmo R. Oliveira_, May 29 2024 %e A185118 The null graph is vacuously 2-regular and, being acyclic, has infinite girth. %e A185118 There are no 2-regular simple graphs with 1 or 2 vertices. %e A185118 The n-cycle has girth n. %Y A185118 2-regular simple graphs with girth at least 8: this sequence (connected), A185228 (disconnected), A185328 (not necessarily connected). %Y A185118 Connected k-regular simple graphs with girth at least 8: A186728 (any k), A186718 (triangle); specific k: this sequence (k=2), A014376 (k=3). %Y A185118 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), this sequence (g=8), A185119 (g=9). %Y A185118 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). %K A185118 nonn,easy %O A185118 0 %A A185118 _Jason Kimberley_, Jan 28 2011 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE