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A163310 a(n) = 20*a(n-1) - 95*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

%I A163310 #8 Sep 08 2022 08:45:46
%S A163310 1,11,125,1455,17225,206275,2489125,30186375,367260625,4477506875,
%T A163310 54660378125,667844409375,8164152265625,99837826421875,
%U A163310 1221162063203125,14938647753984375,182762559075390625,2236079644879296875
%N A163310 a(n) = 20*a(n-1) - 95*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
%C A163310 Binomial transform of A163309. Tenth binomial transform of A074872.
%H A163310 G. C. Greubel, <a href="/A163310/b163310.txt">Table of n, a(n) for n = 0..915</a>
%H A163310 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-95).
%F A163310 a(n) = ((5+sqrt(5))*(10+sqrt(5))^n + (5-sqrt(5))*(10-sqrt(5))^n)/10.
%F A163310 G.f.: (1-9*x)/(1-20*x+95*x^2).
%F A163310 E.g.f.: (1/5)*exp(10*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - _G. C. Greubel_, Dec 18 2016
%t A163310 LinearRecurrence[{20,-95}, {1,11}, 50] (* _G. C. Greubel_, Dec 18 2016 *)
%o A163310 (Magma) [ n le 2 select 10*n-9 else 20*Self(n-1)-95*Self(n-2): n in [1..18] ];
%o A163310 (PARI) Vec((1-9*x)/(1-20*x+95*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 18 2016
%Y A163310 Cf. A163309, A074872.
%K A163310 nonn,easy
%O A163310 0,2
%A A163310 _Klaus Brockhaus_, Jul 24 2009