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%I A165324 #6 Nov 20 2020 17:08:30
%S A165324 1,9,90,981,11349,136170,1667961,20661489,257463450,3218224941,
%T A165324 40291734429,504866733930,6328837455921,79353706214169,
%U A165324 995084584139610,12478956895304901,156498329695484709,1962672755694512490
%N A165324 a(0)=1, a(1)=9, a(n)= 19*a(n-1)-81*a(n-2) for n>1.
%C A165324 a(n)/a(n-1) tends to (19+sqrt(37))/2 = 12.5413812...
%H A165324 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (19,-81).
%F A165324 G.f.: (1-10x)/(1-19x+81x^2). a(n)= Sum_{k, 0<=k<=n}A165253(n,k)*9^(n-k).
%F A165324 a(n) = ((37-sqrt(37))*(19+sqrt(37))^n+(37+sqrt(37))*(19-sqrt(37))^n)/(74*2^n). [From _Klaus Brockhaus_, Sep 28 2009]
%t A165324 LinearRecurrence[{19,-81},{1,9},20] (* _Harvey P. Dale_, Nov 20 2020 *)
%K A165324 nonn
%O A165324 0,2
%A A165324 _Philippe Deléham_, Sep 14 2009

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