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%I #22 Feb 27 2019 05:16:55
%S 0,1,1,2,4,6,12,20,36,64,112,200,352,624,1104,1952,3456,6112,10816,
%T 19136,33856,59904,105984,187520,331776,587008,1038592,1837568,
%U 3251200,5752320,10177536,18007040,31859712,56369152,99733504,176457728
%N a(n) = 2*a(n-2) + 2*a(n-3).
%C 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
%H Noriaki Sannomiya, H Katsura, Y Nakayama, <a href="http://arxiv.org/abs/1612.02285">Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion</a>, arXiv preprint arXiv:1612.02285, 2016. See Table II, line 1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KingGraph.html">King Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalVertexCover.html">Minimal Vertex Cover</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2).
%F G.f.: x*(1+x)/(1-2*x^2-2*x^3).
%F a(n) = (-1)^(n+1)*A078025(n-1).
%F Limit a(n)/a(n-1) = 1.7692923... .
%F a(n)+a(n+1) = A061279(n). - _R. J. Mathar_, Dec 01 2011
%t 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}]
%t LinearRecurrence[{0, 2, 2}, {0, 1, 1}, 40] (* _Harvey P. Dale_, May 07 2014 *)
%t Table[RootSum[-2 - 2 # + #^3 &, 5 #^n + 8 #^(n + 1) + #^(n + 2) &]/19, {n, 20}] (* _Eric W. Weisstein_, Aug 07 2017 *)
%t 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 *)
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_, May 24 2005
%E Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
%E First Mathematica program edited and corrected by _Harvey P. Dale_, May 07 2014
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