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A163308 a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

%I A163308 #10 Sep 08 2022 08:45:46
%S A163308 1,9,85,829,8249,83073,842477,8578325,87547057,894631737,9148831429,
%T A163308 93598030381,957787431785,9802315116081,100327583381981,
%U A163308 1026904742262917,10511148456669793,107590995513204585
%N A163308 a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
%C A163308 Binomial transform of A163307. Inverse binomial transform of A163309.
%H A163308 G. C. Greubel, <a href="/A163308/b163308.txt">Table of n, a(n) for n = 0..985</a>
%H A163308 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -59).
%F A163308 a(n) = ((5+sqrt(5))*(8+sqrt(5))^n + (5-sqrt(5))*(8-sqrt(5))^n)/10.
%F A163308 G.f.: (1-7*x)/(1-16*x+59*x^2).
%F A163308 E.g.f.: (1/5)*exp(8*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - _G. C. Greubel_, Dec 18 2016
%t A163308 LinearRecurrence[{16,-59},{1,9},20] (* _Harvey P. Dale_, Dec 06 2013 *)
%o A163308 (Magma) [ n le 2 select 8*n-7 else 16*Self(n-1)-59*Self(n-2): n in [1..18] ];
%o A163308 (PARI) Vec((1-7*x)/(1-16*x+59*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 18 2016
%Y A163308 Cf. A163307, A163309.
%K A163308 nonn
%O A163308 0,2
%A A163308 _Klaus Brockhaus_, Jul 24 2009