%I #5 Feb 10 2020 21:47:43
%S 1,2,6,8,22,40,82,176,340,722,1450,2966,6096,12362,25384,51728,105698,
%T 216074,440962,901396,1840686,3760232,7681828,15689962,32053346,
%U 65473214,133745304,273208346,558081744,1140024080,2328745042,4757002434,9717279194,19849727740
%N Number of maximal independent sets in the 3 X n king graph.
%H Andrew Howroyd, <a href="/A332348/b332348.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,1,-2,2,-2).
%F a(n) = a(n-1) + 2*a(n-2) + a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) for n >= 6.
%F G.f.: (1 + x + 2*x^2 - 3*x^3 + 2*x^4 - 2*x^5)/(1 - x - 2*x^2 - x^3 + 2*x^4 - 2*x^5 + 2*x^6).
%o (PARI) Vec((1 + x + 2*x^2 - 3*x^3 + 2*x^4 - 2*x^5)/(1 - x - 2*x^2 - x^3 + 2*x^4 - 2*x^5 + 2*x^6) + O(x^40))
%Y Row n=3 of A332347.
%K nonn,easy
%O 0,2
%A _Andrew Howroyd_, Feb 10 2020