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Number of edge covers in the 2 X n king graph.
1

%I #12 Jan 10 2020 10:15:59

%S 1,41,1201,36281,1094401,33014921,995960401,30045123161,906370788001,

%T 27342474236201,824840018262001,24882936703189241,750643185668251201,

%U 22644641945255809481,683120580615598976401,20607688511425541428121,621671836326816125138401

%N Number of edge covers in the 2 X n king graph.

%H Andrew Howroyd, <a href="/A297349/b297349.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/KingGraph.html">King Graph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (29,36,-24).

%F a(n) = 29*a(n-1) + 36*a(n-2) - 24*a(n-3) for n > 3.

%F G.f.: x*(1 + 12*x - 24*x^2)/(1 - 29*x - 36*x^2 + 24*x^3).

%t (* Start from _Eric W. Weisstein_, Dec 29 2017 *)

%t Table[-RootSum[24 - 36 # - 29 #^2 + #^3 &, -9152 #^n - 1682 #^(n + 1) + 65 #^(n + 2) &]/16889, {n, 20}]

%t -RootSum[24 - 36 # - 29 #^2 + #^3 &, #^Range[20] (-9152 - 1682 # + 65 #^2) &]/16889

%t LinearRecurrence[{29, 36, -24}, {1, 41, 1201}, 20]

%t CoefficientList[Series[(1 + 12 x - 24 x^2)/(1 - 29 x - 36 x^2 + 24 x^3), {x, 0, 20}], x]

%t (* End *)

%o (PARI) Vec(x*(1 + 12*x - 24*x^2)/(1 - 29*x - 36*x^2 + 24*x^3) + O(x^20))

%Y Row 2 of A297205.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Dec 28 2017