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A033483 Number of disconnected 4-valent (or quartic) graphs with n nodes. 17
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 378, 2026, 13351, 104595, 930586, 9124662, 96699987, 1095469608, 13175272208, 167460699184, 2241578965849, 31510542635443, 464047929509794, 7143991172244290, 114749135506381940, 1919658575933845129, 33393712487076999918, 603152722419661386031 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,13
REFERENCES
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
LINKS
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Disconnected Graph
Eric Weisstein's World of Mathematics, Quartic Graph
FORMULA
a(n) = A033301(n) - A006820(n) = Euler_transformation(A006820) - A006820.
a(n) = A068933(n, 4). - Jason Kimberley, Sep 27 2009 and Jan 08 2011
MATHEMATICA
A006820 = Cases[Import["https://oeis.org/A006820/b006820.txt", "Table"], {_, _}][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A006820] - A006820 (* Jean-François Alcover, Jan 21 2020, updated Mar 17 2020 *)
CROSSREFS
4-regular simple graphs: A006820 (connected), this sequence (disconnected), A033301 (not necessarily connected). - Jason Kimberley, Jan 08 2011
Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), this sequence (k=4), A165655 (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).
Disconnected 4-regular simple graphs with girth at least g: this sequence (g=3), A185244 (g=4), A185245 (g=5), A185246 (g=6).
Sequence in context: A244278 A190343 A185043 * A130522 A006219 A353406
KEYWORD
nonn,nice,hard
AUTHOR
Ronald C. Read
EXTENSIONS
Terms a(16)-a(18) from Martin Fuller, Dec 04 2006
Terms a(19)-a(26) from Jason Kimberley, Sep 27 2009 and Dec 30 2010
Terms a(27)-a(33), due to the extension of A006820 by Andrew Howroyd, from Jason Kimberley, Mar 12 2020
STATUS
approved

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Last modified February 27 21:03 EST 2024. Contains 370378 sequences. (Running on oeis4.)