A290470 - OEIS

%I #18 Aug 06 2017 22:46:47

%S 3,7,15,59,143,367,1039,2755,7395,20007,53727,144635,389535,1048159,

%T 2821535,7595267,20443523,55029319,148125295,398712379,1073232175,

%U 2888862159,7776059055,20931132355,56341155043,151655701607,408217663167,1098815603707,2957725352255

%N Number of minimal edge covers in the n-Moebius ladder.

%H Andrew Howroyd, <a href="/A290470/b290470.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/MinimalEdgeCover.html">Minimal Edge Cover</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</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 04 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 + x)*(1 + 4*x^3 - 3*x^4)*(3 + x + x^2 - x^3)/((1 + x^2)*(1 + x + x^2 - x^3)*(1 - 2*x - 2*x^2 + x^4)).

%F (End)

%t Table[2 Cos[n Pi/2] - RootSum[-1 + # + #^2 + #^3 &, #^n &] +

%t   RootSum[1 - 2 #^2 - 2 #^3 + #^4 &, #^n &], {n, 20}]

%t LinearRecurrence[{1, 2, 6, 2, 2, -2, -2, -1, 1}, {3, 7, 15, 59, 143, 367, 1039, 2755, 7395}, 20]

%t CoefficientList[Series[-(((1 + x) (-3 - x - x^2 + x^3) (-1 - 4 x^3 + 3 x^4))/((1 + x^2) (-1 - x - x^2 + x^3) (1 - 2 x - 2 x^2 + x^4))), {x, 0, 20}], x]

%o (PARI) Vec((1 + x)*(1 + 4*x^3 - 3*x^4)*(3 + x + x^2 - x^3)/((1 + x^2)*(1 + x + x^2 - x^3)*(1 - 2*x - 2*x^2 + x^4)) + O(x^30)) \\ _Andrew Howroyd_, Aug 04 2017

%Y Cf. A020866, A020877, A020878, A284710.

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Aug 03 2017

%E a(1)-a(2) and terms a(9) and beyond from _Andrew Howroyd_, Aug 04 2017