%I #15 Feb 18 2024 10:13:04
%S 8,16,35,80,188,451,1100,2720,6803,17176,43700,111875,287828,743416,
%T 1926035,5001920,13014188,33909571,88452380,230923280,603268883,
%U 1576786216,4122895460,10783511555,28210861988,73815519976,193168589075,505556029520,1323231064028
%N a(n) = Lucas(2*n) + 2^(n + 1) + 1.
%C For n >= 3, the number of independent vertex sets in the n-trapezohedron graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TrapezohedralGraph.html">Trapezohedral Graph</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,9,-2).
%F a(n) = 6*a(n-1) - 12*a(n-2) + 9*a(n-3) - 2*a(n-4).
%F G.f.: x*(8-32*x+35*x^2-10*x^3)/((1-x)*(1-2*x)*(1-3*x+x^2)).
%t Table[LucasL[2 n] + 2^(n + 1) + 1, {n, 20}]
%t LinearRecurrence[{6, -12, 9, -2}, {8, 16, 35, 80}, 20]
%t CoefficientList[Series[(8 - 32 x + 35 x^2 - 10 x^3)/(1 - 6 x + 12 x^2 - 9 x^3 + 2 x^4), {x, 0, 20}], x]
%Y Cf. A005248 (bisection of the Lucas numbers).
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Oct 11 2023