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%I #16 Feb 25 2020 17:54:28
%S 2,18,194,2066,22018,234642,2500546,26647954,283983362,3026369298,
%T 32251576514,343700350226,3662764537858,39033547830162,
%U 415974830066626,4432983135477394,47241655165240322,503447433600744978,5365165922164132034,57175791256846535186
%N Expansion of (2 - 2*x) / (1 - 10*x - 7*x^2).
%H Colin Barker, <a href="/A157765/b157765.txt">Table of n, a(n) for n = 0..900</a>
%H Tomislav Došlić and Frode Måløy, <a href="http://dx.doi.org/10.1016/j.disc.2009.11.026">Chain hexagonal cacti: Matchings and independent sets</a>, Discr. Math., 310 (2010), 1676-1690.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, 7).
%F From _Colin Barker_, Nov 25 2017: (Start)
%F a(n) = ((5-4*sqrt(2))^n*(-1+sqrt(2)) + (1+sqrt(2))*(5+4*sqrt(2))^n) / sqrt(2).
%F a(n) = 10*a(n-1) + 7*a(n-2) for n > 1.
%F (End)
%t CoefficientList[Series[(2-2x)/(1-10x-7x^2),{x,0,30}],x] (* or *) LinearRecurrence[{10,7},{2,18},30] (* _Harvey P. Dale_, Feb 25 2020 *)
%o (PARI) Vec(2*(1 - x) / (1 - 10*x - 7*x^2) + O(x^40)) \\ _Colin Barker_, Nov 25 2017
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, May 22 2010