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A163470 a(n) = 8*a(n-1) - 13*a(n-2) for n > 1; a(0) = 3, a(1) = 15.

%I A163470 #9 Sep 08 2022 08:45:46
%S A163470 3,15,81,453,2571,14679,84009,481245,2757843,15806559,90600513,
%T A163470 519318837,2976744027,17062807335,97804786329,560621795277,
%U A163470 3213512139939,18420013780911,105584452428081,605215440272805
%N A163470 a(n) = 8*a(n-1) - 13*a(n-2) for n > 1; a(0) = 3, a(1) = 15.
%C A163470 Binomial transform of A083881 without initial 1. Inverse binomial transform of A163471.
%H A163470 G. C. Greubel, <a href="/A163470/b163470.txt">Table of n, a(n) for n = 0..1000</a>
%H A163470 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13).
%F A163470 a(n) = ((3+sqrt(3))*(4+sqrt(3))^n + (3-sqrt(3))*(4-sqrt(3))^n)/2.
%F A163470 G.f.: (3-9*x)/(1-8*x+13*x^2).
%F A163470 a(n) = 3*A162557(n). - _R. J. Mathar_, Jun 14 2016
%F A163470 E.g.f.: (1/2)*exp(4*x)*(6*cosh(sqrt(3)*x) + 2*sqrt(3)*sinh(sqrt(3)*x)). - _G. C. Greubel_, Jul 25 2017
%t A163470 LinearRecurrence[{8, -13}, {3, 15}, 50] (* _G. C. Greubel_, Jul 25 2017 *)
%o A163470 (Magma) [ n le 2 select 12*n-9 else 8*Self(n-1)-13*Self(n-2): n in [1..22] ];
%o A163470 (PARI) x='x+O('x^50); Vec((3-9*x)/(1-8*x+13*x^2)) \\ _G. C. Greubel_, Jul 25 2017
%Y A163470 Cf. A083881, A163471.
%K A163470 nonn,easy
%O A163470 0,1
%A A163470 _Klaus Brockhaus_, Aug 11 2009