%I #7 Sep 08 2022 08:45:46

%S 1,11,119,1273,13513,142667,1500479,15737929,164744881,1722111467,

%T 17983160807,187650088633,1957031891641,20402217047531,

%U 212634387415919,2215643826731593,23083472275311073,240466638643803467

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

%C Binomial transform of A163446. Inverse binomial transform of A163448.

%H G. C. Greubel, <a href="/A163447/b163447.txt">Table of n, a(n) for n = 0..975</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-79).

%F a(n) = ((1+sqrt(2))*(9+sqrt(2))^n + (1-sqrt(2))*(9-sqrt(2))^n)/2.

%F G.f.: (1-7*x)/(1-18*x+79*x^2).

%F E.g.f.: exp(9*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 23 2016

%t LinearRecurrence[{18,-79}, {1,11}, 50] (* _G. C. Greubel_, Dec 23 2016 *)

%o (Magma) [ n le 2 select 10*n-9 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];

%o (PARI) Vec((1-7*x)/(1-18*x+79*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 23 2016

%Y Cf. A163446, A163448.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Jul 27 2009