cp's OEIS Frontend

A200069 a(n) = 4*a(n-1) + 13*a(n-2) for n>2, a(1)=1, a(2)=4.

%I A200069 #27 Jul 08 2024 21:42:50
%S A200069 1,4,29,168,1049,6380,39157,239568,1467313,8983636,55009613,336825720,
%T A200069 2062427849,12628445756,77325345061,473471175072,2899114186081,
%U A200069 17751582020260,108694812500093,665549816263752,4075231827556217,24953074921653644,152790313444845397
%N A200069 a(n) = 4*a(n-1) + 13*a(n-2) for n>2, a(1)=1, a(2)=4.
%C A200069 De Moivres formula : a(n)=(r^n-s^n)/(r-s), for r>s gives sequences with integers if r and s are conjugates. With r=2+sqrt(17) and s=2-sqrt(17), a(n+1)/a(n) converges to 2+sqrt(17).
%H A200069 Reinhard Zumkeller, <a href="/A200069/b200069.txt">Table of n, a(n) for n = 1..1000</a>
%H A200069 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,13).
%F A200069 a(n) = ((2+sqrt(17))^n-(2-sqrt(17))^n)/(2*sqrt(17)).
%F A200069 G.f.: x/(1-4*x-13*x^2). - _Bruno Berselli_, Nov 15 2011
%e A200069 a(3) = 4*4+13*1 = 29.
%t A200069 LinearRecurrence[{4,13}, {1,4}, 50]
%o A200069 (Haskell)
%o A200069 a200069 n = a200069_list !! (n-1)
%o A200069 a200069_list = 1 : 4 : zipWith (+)
%o A200069    (map (* 4) $ tail a200069_list) (map (* 13) a200069_list)
%o A200069 -- _Reinhard Zumkeller_, Nov 15 2011
%Y A200069 Cf. A041025.
%K A200069 nonn,easy
%O A200069 1,2
%A A200069 _Sture Sjöstedt_, Nov 13 2011
%E A200069 More terms from _Bruno Berselli_, Nov 15 2011