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A163474 a(n) = 16*a(n-1) - 61*a(n-2) for n > 1; a(0) = 3, a(1) = 27.

%I A163474 #9 Sep 08 2022 08:45:46
%S A163474 3,27,249,2337,22203,212691,2048673,19804617,191904819,1862395467,
%T A163474 18092133513,175868012721,1710268059243,16636340171907,
%U A163474 161855091136689,1574864707700697,15324674763873123,149128049052227451
%N A163474 a(n) = 16*a(n-1) - 61*a(n-2) for n > 1; a(0) = 3, a(1) = 27.
%C A163474 Binomial transform of A163473. Inverse binomial transform of A163475.
%H A163474 G. C. Greubel, <a href="/A163474/b163474.txt">Table of n, a(n) for n = 0..1000</a>
%H A163474 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-61).
%F A163474 a(n) = ((3+sqrt(3))*(8+sqrt(3))^n + (3-sqrt(3))*(8-sqrt(3))^n)/2.
%F A163474 G.f.: (3-21*x)/(1-16*x+61*x^2).
%F A163474 E.g.f.: exp(8*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - _G. C. Greubel_, Jul 26 2017
%t A163474 LinearRecurrence[{16, -61}, {3, 27}, 50] (* _G. C. Greubel_, Jul 26 2017 *)
%o A163474 (Magma) [ n le 2 select 24*n-21 else 16*Self(n-1)-61*Self(n-2): n in [1..18] ];
%o A163474 (PARI) x='x+O('x^50); Vec((3-21*x)/(1-16*x+61*x^2)) \\ _G. C. Greubel_, Jul 26 2017
%Y A163474 Cf. A163473, A163475.
%K A163474 nonn
%O A163474 0,1
%A A163474 _Klaus Brockhaus_, Aug 11 2009