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%I #23 Sep 08 2022 08:46:00
%S 32,1508,70844,3328160,156352676,7345247612,345070285088,
%T 16210958151524,761569962836540,35777577295165856,1680784562909958692,
%U 78961096879472892668,3709490768772315996704,174267105035419378952420,8186844445895938494767036
%N a(n) = Fibonacci(8n+7) mod Fibonacci(8n+1).
%H Vincenzo Librandi, <a href="/A200258/b200258.txt">Table of n, a(n) for n = 1..600</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (47,-1).
%F From _Bruno Berselli_, Nov 17 2011: (Start)
%F G.f.: 4*x*(8+x)/(1-47*x+x^2).
%F a(n) = 47*a(n-1)-a(n-2).
%F a(n) = ((-5+3r)*(47+21r)^n-(5+3r)*(47-21r)^n)/(5*2^(n-1)) where r=sqrt(5). (End)
%F a(n) = 32*A049668(n) + 4*A049668(n-1). - _R. J. Mathar_, Nov 26 2011
%t Table[Mod[Fibonacci[(8 n + 7)] , Fibonacci[(8 n + 1)]], {n, 1, 16}]
%t CoefficientList[Series[4*(8+x)/(1-47*x+x^2),{x,0,20}],x] (* _Vincenzo Librandi_, Jul 12 2012 *)
%o (Magma) I:=[32, 1508]; [n le 2 select I[n] else 47*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jul 12 2012
%K nonn,easy
%O 1,1
%A _Artur Jasinski_, Nov 15 2011
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