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A185336
Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 6.
4
1, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7574, 181227, 4624502, 122090545, 3328929960, 93990692632, 2754222605808
OFFSET
0,10
COMMENTS
The null graph on 0 vertices is vacuously 3-regular; since it is acyclic, it has infinite girth.
FORMULA
Euler transformation of A014374.
MATHEMATICA
A014374 = Cases[Import["https://oeis.org/A014374/b014374.txt", "Table"], {_, _}][[All, 2]];
etr[f_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d f[d], {d, Divisors[j]}] b[n - j], {j, 1, n}]/n]; b];
a = etr[A014374[[# + 1]]&];
a /@ Range[0, Length[A014374] - 1] (* Jean-François Alcover, Dec 04 2019 *)
CROSSREFS
3-regular simple graphs with girth at least 6: A014374 (connected), A185236 (disconnected), this sequence (not necessarily connected).
Not necessarily connected k-regular simple graphs with girth at least 6: A185326 (k=2), this sequence (k=3).
Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), A185334 (g=4), A185335 (g=5), this sequence (g=6).
Not necessarily connected 3-regular simple graphs with girth *exactly* g: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).
Sequence in context: A006926 A185136 A014374 * A125709 A363314 A203112
KEYWORD
nonn,more,hard
AUTHOR
Jason Kimberley, Jan 28 2012
EXTENSIONS
a(18) from A014374 from Jean-François Alcover, Dec 04 2019
STATUS
approved