OFFSET
0,4
COMMENTS
Also the number of maximal independent vertex sets (and minimal vertex covers) in the 2 X (n-2) king graph. - Eric W. Weisstein, Aug 07 2017
LINKS
Noriaki Sannomiya, H Katsura, Y Nakayama, Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion, arXiv preprint arXiv:1612.02285, 2016. See Table II, line 1.
Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set
Eric Weisstein's World of Mathematics, Minimal Vertex Cover
Index entries for linear recurrences with constant coefficients, signature (0,2,2).
FORMULA
G.f.: x*(1+x)/(1-2*x^2-2*x^3).
a(n) = (-1)^(n+1)*A078025(n-1).
Limit a(n)/a(n-1) = 1.7692923... .
a(n)+a(n+1) = A061279(n). - R. J. Mathar, Dec 01 2011
MATHEMATICA
m = 2; a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 2; a[n_] := a[n] = a[n - 1] + m*a[n - 2] - m*a[n - 4]; Table[a[n], {n, 0, 50}]
LinearRecurrence[{0, 2, 2}, {0, 1, 1}, 40] (* Harvey P. Dale, May 07 2014 *)
Table[RootSum[-2 - 2 # + #^3 &, 5 #^n + 8 #^(n + 1) + #^(n + 2) &]/19, {n, 20}] (* Eric W. Weisstein, Aug 07 2017 *)
CoefficientList[Series[-((2 (1 + 2 x + x^2))/(-1 + 2 x^2 + 2 x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 07 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, May 24 2005
EXTENSIONS
Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
First Mathematica program edited and corrected by Harvey P. Dale, May 07 2014
STATUS
approved