%I #14 Jul 17 2022 23:27:17
%S 2,8,12,16,30,48,74,124,200,320,522,844,1362,2208,3572,5776,9350,
%T 15128,24474,39604,64080,103680,167762,271444,439202,710648,1149852,
%U 1860496,3010350,4870848,7881194,12752044,20633240,33385280,54018522,87403804,141422322
%N Number of maximal independent vertex sets (and minimal vertex covers) in the n-Moebius ladder graph.
%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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,2,1).
%F a(n) = Lucas(n) - 2*cos(2*n*Pi/3).
%F a(n) = a(n-2) + 2*a(n-3) + a(n-4).
%F G.f.: -((2 x (1 + 4 x + 5 x^2 + 2 x^3))/(-1 + x^2 + 2 x^3 + x^4)).
%t Table[LucasL[n] - 2 Cos[2 n Pi/3], {n, 3, 20}]
%t LinearRecurrence[{0, 1, 2, 1}, {2, 8, 12, 16}, 20]
%t CoefficientList[Series[-((2 (1 + 4 x + 5 x^2 + 2 x^3))/(-1 + x^2 + 2 x^3 + x^4)), {x, 0, 20}], x]
%Y Cf. A000032.
%K nonn,easy
%O 3,1
%A _Eric W. Weisstein_, Aug 07 2017