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A185117
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Number of connected 2-regular simple graphs on n vertices with girth at least 7.
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13
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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
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OFFSET
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0
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COMMENTS
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LINKS
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FORMULA
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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.
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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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MATHEMATICA
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PadRight[{1, 0, 0, 0, 0, 0, 0}, 100, 1] (* Paolo Xausa, Jun 30 2024 *)
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CROSSREFS
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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).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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