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%I #25 Apr 01 2017 05:33:13
%S 41,265,1697,10897,69941,448945,2881697,18497137,118730021,762108145,
%T 4891844657,31399932337,201550911701,1293721577905,8304182337857,
%U 53303156937457,342144045482501,2196165379031665,14096818096762577,90485116626705457,580808823292457141
%N Number of strong edge-subgraphs in Moebius ladder M_n.
%C Also known as the number of edge covers in the Moebius ladder M_n. - _Eric W. Weisstein_, Mar 31 2017
%H Colin Barker, <a href="/A020866/b020866.txt">Table of n, a(n) for n = 2..1000</a>
%H J. P. McSorley, <a href="http://dx.doi.org/10.1016/S0012-365X(97)00086-1">Counting structures in the Moebius ladder</a>, Discrete Math., 184 (1998), 137-164.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,9,1,-2).
%F a(n) = Lucas(2n) + [x^n] x(4+2x+3x^2-4x^3+x^4)/((1+x)(1-3x+x^2)(1-6x-3x^2+2x^3)); a(n) ~ (6.4188)^n + (-0.8056)^n + (0.3867)^n - (- 1)^n (Th. 3.2.). - C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005
%F From _R. J. Mathar_, Feb 06 2010: (Start)
%F a(n) = 5*a(n-1) + 9*a(n-2) + a(n-3) - 2*a(n-4).
%F G.f.: -x^2*(-41-60*x-3*x^2+14*x^3)/ ((1+x) * (2*x^3-3*x^2-6*x+1)). (End)
%p with(combinat): lucas:= n->fibonacci(n+1)+fibonacci(n-1):seq(lucas(2*n)+coeff(convert(series(x*(4+2*x+3*x^2-4*x^3+x^4)/((1+x)*(1-3*x+x^2)*(1-6*x-3*x^2+2*x^3)),x,50),polynom),x,n),n=2..25); # C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005
%t Table[RootSum[2 - 3 # - 6 #^2 + #^3 &, #^n &] - (-1)^n, {n, 2, 20}] (* _Eric W. Weisstein_, Mar 31 2017 *)
%t LinearRecurrence[{5, 9, 1, -2}, {41, 265, 1697, 10897}, 20] (* _Eric W. Weisstein_, Mar 31 2017 *)
%o (PARI) Vec(-x^2*(14*x^3-3*x^2-60*x-41)/((x+1)*(2*x^3-3*x^2-6*x+1)) + O(x^30)) \\ _Colin Barker_, Aug 02 2015
%K nonn,easy
%O 2,1
%A _N. J. A. Sloane_
%E More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005
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