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

%I

%S 1,11,125,1455,17225,206275,2489125,30186375,367260625,4477506875,

%T 54660378125,667844409375,8164152265625,99837826421875,

%U 1221162063203125,14938647753984375,182762559075390625,2236079644879296875

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

%C Binomial transform of A163309. Tenth binomial transform of A074872.

%H G. C. Greubel, <a href="/A163310/b163310.txt">Table of n, a(n) for n = 0..915</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-95).

%F a(n) = ((5+sqrt(5))*(10+sqrt(5))^n + (5-sqrt(5))*(10-sqrt(5))^n)/10.

%F G.f.: (1-9*x)/(1-20*x+95*x^2).

%F 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 LinearRecurrence[{20,-95}, {1,11}, 50] (* _G. C. Greubel_, Dec 18 2016 *)

%o (MAGMA) [ n le 2 select 10*n-9 else 20*Self(n-1)-95*Self(n-2): n in [1..18] ];

%o (PARI) Vec((1-9*x)/(1-20*x+95*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 18 2016

%Y Cf. A163309, A074872.

%K nonn,easy

%O 0,2

%A _Klaus Brockhaus_, Jul 24 2009

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Last modified June 18 01:16 EDT 2021. Contains 345098 sequences. (Running on oeis4.)