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%I #12 Aug 01 2015 08:59:42
%S 1,18,98,812,5748,43120,316600,2343120,17290256,127726400,943159584,
%T 6965532736,51439836352,379886330112,2805462584192,20718413985536,
%U 153005867110656,1129951564794880,8344715027364352,61625891492889600
%N Expansion of (1+12*x-24*x^2+8*x^4)/((1-8*x+4*x^2+4*x^3)*(1+2*x-2*x^2)).
%D S. Kitaev, A. Burstein and T. Mansour. Counting independent sets in certain classes of (almost) regular graphs, Pure Mathematics and Applications (PU.M.A.) 19 (2008), no. 2-3, 17-26.
%H S. Kitaev, A. Burstein and T. Mansour. <a href="http://www.ru.is/kennarar/sergey/index_files/Papers/burkitman_PUMA.pdf"> Counting independent sets in certain classes of (almost) regular graphs </a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6, 14, -28, 0, 8).
%F From _Harvey P. Dale_, May 09 2011: (Start)
%F G.f.: (1+12*x-24*x^2+8*x^4)/((1-8*x+4*x^2+4*x^3)*(1+2*x-2*x^2)).
%F a(0)=1, a(1)=18, a(2)=98, a(3)=812, a(4)=5748, a(n)=6a(n-1)+ 14a(n-2) -28a(n-3) +8a(n-5). (End)
%t CoefficientList[Series[(1+12x-24x^2+8x^4)/((1-8x+4x^2+4x^3)(1+2x-2x^2)),{x,0,20}],x] (* or *) LinearRecurrence[{6,14,-28,0,8},{1,18,98,812, 5748},20] (* _Harvey P. Dale_, May 09 2011 *)
%K nonn
%O 0,2
%A Signy Olafsdottir (signy06(AT)ru.is), May 07 2010
%E Definition clarified by _Harvey P. Dale_, May 09 2011