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%I #13 Aug 11 2017 10:57:41
%S 1,5,25,49,141,389,1009,2761,7441,19925,53769,144721,389325,1048325,
%T 2821665,7594761,20444065,55029413,148124153,398713969,1073231821,
%U 2888859781,7776063377,20931130057,56341150641,151655712629,408217654249,1098815597201
%N Number of minimal edge covers in the n-prism graph.
%C The n-prism graph is well defined for n >= 3. Sequence extended to n = 1 using recurrence. - _Andrew Howroyd_, Aug 10 2017
%H Andrew Howroyd, <a href="/A290700/b290700.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalEdgeCover.html">Minimal Edge Cover</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, 6, 2, 2, -2, -2, -1, 1).
%F From _Andrew Howroyd_, Aug 10 2017: (Start)
%F a(n) = a(n-1) + 2*a(n-2) + 6*a(n-3) + 2*a(n-4) + 2*a(n-5) - 2*a(n-6) - 2*a(n-7) - a(n-8) + a(n-9) for n > 9.
%F G.f.: x*(1 + 4*x + 18*x^2 + 8*x^3 + 10*x^4 - 12*x^5 - 14*x^6 - 8*x^7 + 9*x^8)/((1 - 2*x - 2*x^2 + x^4)*(1 + x + x^2 - x^3)*(1 + x^2)).
%F (End)
%t Table[2 Cos[n Pi/2] + RootSum[-1 + # + #^2 + #^3 &, #^n &] -
%t RootSum[1 - 2 #^2 - 2 #^3 + #^4 &, -2 #^(n + 2) - 2 #^(n + 3) + #^(n + 4) &], {n, 20}]
%t LinearRecurrence[{1, 2, 6, 2, 2, -2, -2, -1, 1}, {1, 5, 25, 49, 141, 389, 1009, 2761, 7441}, 20]
%t CoefficientList[Series[-( (1 + 4 x + 18 x^2 + 8 x^3 + 10 x^4 - 12 x^5 - 14 x^6 - 8 x^7 + 9 x^8)/((1 + x^2) (-1 - x - x^2 + x^3) (1 - 2 x - 2 x^2 + x^4))), {x, 0, 20}], x]
%o (PARI)
%o Vec((1 + 4*x + 18*x^2 + 8*x^3 + 10*x^4 - 12*x^5 - 14*x^6 - 8*x^7 + 9*x^8)/((1 - 2*x - 2*x^2 + x^4)*(1 + x + x^2 - x^3)*(1 + x^2))+O(x^30)) \\ _Andrew Howroyd_, Aug 10 2017
%Y Cf. A123304.
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Aug 09 2017
%E a(1)-a(2) and terms a(9) and beyond from _Andrew Howroyd_, Aug 10 2017
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