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A185115
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Number of connected 2-regular simple graphs on n vertices with girth at least 5.
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14
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1, 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, 1
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OFFSET
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0
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LINKS
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Table of n, a(n) for n=0..101.
Jason Kimberley, Connected regular graphs with girth at least 5
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
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FORMULA
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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.
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EXAMPLE
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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.
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CROSSREFS
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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).
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: A204545 A185116 A205809 * A181923 A195376 A188189
Adjacent sequences: A185112 A185113 A185114 * A185116 A185117 A185118
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KEYWORD
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nonn,easy
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AUTHOR
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Jason Kimberley, Jan 28 2011
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STATUS
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approved
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