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