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A107383
a(n) = 2*a(n-2) + 2*a(n-3).
2
0, 1, 1, 2, 4, 6, 12, 20, 36, 64, 112, 200, 352, 624, 1104, 1952, 3456, 6112, 10816, 19136, 33856, 59904, 105984, 187520, 331776, 587008, 1038592, 1837568, 3251200, 5752320, 10177536, 18007040, 31859712, 56369152, 99733504, 176457728
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
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
Sequence in context: A329227 A294430 A294429 * A078025 A178901 A164146
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