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 A185114 Number of connected 2-regular simple graphs on n vertices with girth at least 4. 19
 1, 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, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 LINKS Jason Kimberley, Connected regular graphs with girth at least 4 FORMULA a(0)=1; for 0=4 , a(n)=1. Inverse Euler transformation of A008484. a(n) = A130543(n) + A000007(n). - Bruno Berselli, Jan 31 2011 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 a[n_] := Switch[n, 0, 1, 1|2|3, 0, _, 1]; a /@ Range[0, 101] (* Jean-François Alcover, Dec 05 2019 *) CROSSREFS 2-regular simple graphs with girth at least 4: this sequence (connected), A185224 (disconnected), A008484 (not necessarily connected). Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: this sequence (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9). Connected 2-regular simple graphs with girth at least g: A179184 (g=3), this sequence (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: A138711 A285617 A246500 * A154281 A154282 A224877 Adjacent sequences:  A185111 A185112 A185113 * A185115 A185116 A185117 KEYWORD nonn,easy,changed AUTHOR Jason Kimberley, Jan 27 2011 STATUS approved

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)