%I #11 Feb 18 2024 10:01:57
%S 2,10,17,50,122,325,842,2210,5777,15130,39602,103685,271442,710650,
%T 1860497,4870850,12752042,33385285,87403802,228826130,599074577,
%U 1568397610,4106118242,10749957125,28143753122,73681302250,192900153617,505019158610,1322157322202
%N a(n) = Lucas(2*n) + 2*(-1)^n + 1.
%C For n >=3, number of independent vertex sets in the n-double cone graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DoubleConeGraph.html">Double Cone Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-3,1).
%F a(n) = 3*a(n-1)-3*a(n-3)+a(n-4).
%F G.f.: x*(-2-4*x+13*x^2-5*x^3)/((x+1)*(x-1)*(x^2-3*x+1)).
%t Table[LucasL[2 n] + 2 (-1)^n + 1, {n, 20}]
%t LinearRecurrence[{3, 0, -3, 1}, {2, 10, 17, 50}, 20]
%t CoefficientList[Series[(-2 - 4 x + 13 x^2 - 5 x^3)/(-1 + 3 x - 3 x^3 + 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