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A163447 a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

%I A163447 #7 Sep 08 2022 08:45:46
%S A163447 1,11,119,1273,13513,142667,1500479,15737929,164744881,1722111467,
%T A163447 17983160807,187650088633,1957031891641,20402217047531,
%U A163447 212634387415919,2215643826731593,23083472275311073,240466638643803467
%N A163447 a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
%C A163447 Binomial transform of A163446. Inverse binomial transform of A163448.
%H A163447 G. C. Greubel, <a href="/A163447/b163447.txt">Table of n, a(n) for n = 0..975</a>
%H A163447 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-79).
%F A163447 a(n) = ((1+sqrt(2))*(9+sqrt(2))^n + (1-sqrt(2))*(9-sqrt(2))^n)/2.
%F A163447 G.f.: (1-7*x)/(1-18*x+79*x^2).
%F A163447 E.g.f.: exp(9*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 23 2016
%t A163447 LinearRecurrence[{18,-79}, {1,11}, 50] (* _G. C. Greubel_, Dec 23 2016 *)
%o A163447 (Magma) [ n le 2 select 10*n-9 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];
%o A163447 (PARI) Vec((1-7*x)/(1-18*x+79*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 23 2016
%Y A163447 Cf. A163446, A163448.
%K A163447 nonn
%O A163447 0,2
%A A163447 _Klaus Brockhaus_, Jul 27 2009