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%I #6 Jun 13 2015 00:53:37
%S 1,7,21,87,317,1215,4565,17287,65261,246671,931909,3521367,13305053,
%T 50272991,189953717,717732903,2711921613,10246881583,38717399589,
%U 146292038647
%N Expansion of g.f.: (1+4*x-4*x^2)/(1-3*x-4*x^2+4*x^3)
%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 Harvey P. Dale, <a href="/A177369/b177369.txt">Table of n, a(n) for n = 1..1000</a>
%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_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,4,-4).
%F G.f.:(1+4*x-4*x^2)/(1-3*x-4*x^2+4*x^3)
%F a(1)=1, a(2)=7, a(3)=21, a(n)=3*a(n-1)+4*a(n-2)-4*a(n-3). - _Harvey P. Dale_, May 10 2015
%t CoefficientList[Series[(1+4x-4x^2)/(1-3x-4x^2+4x^3),{x,0,20}],x] (* or *) LinearRecurrence[{3,4,-4},{1,7,21},20] (* _Harvey P. Dale_, May 10 2015 *)
%K nonn
%O 1,2
%A Signy Olafsdottir (signy06(AT)ru.is), May 07 2010
%E Definition clarified by _Harvey P. Dale_, May 10 2015
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