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%I #14 Jul 04 2023 13:52:48
%S 1,7,43,277,1777,11407,73219,469981,3016729,19363879,124293499,
%T 797819173,5121067777,32871277183,210995228083,1354343064493,
%U 8693301516841,55800847838359,358176305451691,2299073773191541,14757369859827601,94725087867636847
%N Number of edge covers in the ladder graph P_2 x P_n.
%H Andrew Howroyd, <a href="/A286911/b286911.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6, 3, -2).
%F a(n) = 6*a(n-1) + 3*a(n-2) - 2*a(n-3) for n > 3.
%F G.f.: x*(1-x)*(1+2*x)/(1-6*x-3*x^2+2*x^3).
%t Table[-RootSum[2 - 3 # - 6 #^2 + #^3 &, -14 #^n - 5 #^(n + 1) + #^(n + 2) &]/30, {n, 20}] (* _Eric W. Weisstein_, Aug 09 2017 *)
%t LinearRecurrence[{6, 3, -2}, {1, 7, 43}, 20] (* _Eric W. Weisstein_, Aug 09 2017 *)
%t CoefficientList[Series[(1 + x - 2 x^2)/(1 - 6 x - 3 x^2 + 2 x^3), {x, 0, 20}], x] (* _Eric W. Weisstein_, Aug 09 2017 *)
%Y Row 2 of A286912.
%Y Cf. A123304, A020866.
%K nonn
%O 1,2
%A _Andrew Howroyd_, May 15 2017