%I #13 Dec 24 2017 15:55:40
%S 6,52,360,2576,18336,130624,930432,6627584,47208960,336274432,
%T 2395318272,17062105088,121535176704,865707900928,6166528819200,
%U 43924836122624,312881247289344,2228686172717056,15875167014617088,113080491469438976
%N Number of edge covers on the n-web graph.
%C Extended to a(1)-a(2) using the formula/recurrence.
%H Colin Barker, <a href="/A287082/b287082.txt">Table of n, a(n) for n = 1..1000</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/WebGraph.html">Web Graph</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,8).
%F a(n) = (3-sqrt(17))^n + (3+sqrt(17))^n.
%F G.f.: -((2*x*(3+8*x))/(-1+6*x+8*x^2)).
%F a(n) = 6*a(n-1) + 8*a(n-2) for n>2. - _Colin Barker_, May 20 2017
%F a(n) = I^n*2^((3*n + 2)/2)*ChebyshevT(n, -3*I/(2*sqrt(2))). - _Eric W. Weisstein_, Dec 24 2017
%t Table[(3 - Sqrt[17])^n + (3 + Sqrt[17])^n, {n, 20}] // Expand
%t LinearRecurrence[{6, 8}, {6, 52}, 20]
%t CoefficientList[Series[-2 (3 + 8 x)/(-1 + 6 x + 8 x^2), {x, 0, 20}], x] (* _Eric W. Weisstein_, Dec 24 2017 *)
%t Table[I^n 2^((3 n + 2)/2) ChebyshevT[n, -3 I/(2 Sqrt[2])], {n, 20}] (* _Eric W. Weisstein_, Dec 24 2017 *)
%o (PARI) Vec(2*x*(3 + 8*x) / (1 - 6*x - 8*x^2) + O(x^30)) \\ _Colin Barker_, May 20 2017
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, May 19 2017