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A163444 a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

%I A163444 #8 Sep 08 2022 08:45:46
%S A163444 1,8,62,472,3556,26624,198584,1477792,10981648,81534848,605042144,
%T A163444 4488320896,33288417856,246858103808,1830491038592,13572716933632,
%U A163444 100635907891456,746158518953984,5532281359138304,41017986665224192
%N A163444 a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
%C A163444 Binomial transform of A163346. Inverse binomial transform of A163445.
%H A163444 G. C. Greubel, <a href="/A163444/b163444.txt">Table of n, a(n) for n = 0..1000</a>
%H A163444 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-34).
%F A163444 a(n) = ((1+sqrt(2))*(6+sqrt(2))^n + (1-sqrt(2))*(6-sqrt(2))^n)/2.
%F A163444 G.f.: (1-4*x)/(1-12*x+34*x^2).
%F A163444 E.g.f.: 2*exp(6*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 23 2016
%t A163444 LinearRecurrence[{12,-34}, {1,8}, 50] (* _G. C. Greubel_, Dec 23 2016 *)
%o A163444 (Magma) [ n le 2 select 7*n-6 else 12*Self(n-1)-34*Self(n-2): n in [1..20] ];
%o A163444 (PARI) Vec((1-4*x)/(1-12*x+34*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 23 2016
%Y A163444 Cf. A163346, A163445.
%K A163444 nonn,easy
%O A163444 0,2
%A A163444 _Klaus Brockhaus_, Jul 27 2009