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A165628
Number of 7-regular graphs (septic graphs) on 2n vertices.
11
1, 0, 0, 0, 1, 5, 1547, 21609301, 733351105935, 42700033549946255, 4073194598236125134140, 613969628444792223023625238, 141515621596238755267618266465449
OFFSET
0,6
COMMENTS
Because the triangle A051031 is symmetric, a(n) is also the number of (2n-8)-regular graphs on 2n vertices.
FORMULA
Euler transformation of A014377.
MATHEMATICA
A014377 = Cases[Import["https://oeis.org/A014377/b014377.txt", "Table"], {_, _}][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A014377] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)
CROSSREFS
7-regular simple graphs: A014377 (connected), A165877 (disconnected), this sequence (not necessarily connected).
Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), this sequence (k=7), A180260 (k=8).
Sequence in context: A184973 A184971 A014377 * A119747 A177906 A127106
KEYWORD
nonn,hard,more
AUTHOR
Jason Kimberley, Sep 22 2009
EXTENSIONS
Cross-references edited by Jason Kimberley, Nov 07 2009 and Oct 17 2011
a(9)-a(11) from Andrew Howroyd, Mar 09 2020
a(12) from Andrew Howroyd, May 19 2020
STATUS
approved