A179184 - OEIS

A179184

Number of connected 2-regular simple graphs with n vertices.

1, 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

COMMENTS

All simple graphs have girth at least 3. Acyclic graphs have infinite girth.

Decimal expansion of 901/9000. - Elmo R. Oliveira, May 28 2024

LINKS

Table of n, a(n) for n=0..99.

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

a(0)=1; for 0 < n < 3 a(n)=0; for n >= 3, a(n)=1.

Proof: The null graph is vacuously 2-regular. There are no 2-regular simple graphs with 1 or 2 vertices. The n-cycle has girth n. QED.

G.f.: (x^3-x+1)/(1-x). - Elmo R. Oliveira, May 28 2024

MATHEMATICA

PadRight[{1, 0, 0}, 100, 1] (* Paolo Xausa, Jun 26 2024 *)

PROG

(Magma) [1, 0, 0, 1^^97];

CROSSREFS

2-regular simple graphs (with girth at least 3): this sequence (connected), A165652 (disconnected), A008483 (not necessarily connected).

2-regular connected: this sequence (simple graphs), A000012 (multigraphs with loops allowed).

Connected regular simple graphs: A005177 (any degree), A068934 (triangular array), specified degree k: this sequence (k=2), A002851 (k=3), A006820 (k=4),A006821 (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).

Connected 2-regular simple graphs with girth at least g: this sequence (g=3), A185115 (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: A331313 A267155 A204445 * A154272 A240465 A240353

Adjacent sequences: A179181 A179182 A179183 * A179185 A179186 A179187

KEYWORD

nonn,easy

AUTHOR

Jason Kimberley, Jan 05 2011

STATUS

approved