A191968 - OEIS

%I #38 Sep 08 2022 08:45:57

%S 29,1364,64079,3010349,141422324,6643838879,312119004989,

%T 14662949395604,688846502588399,32361122672259149,1520283919093591604,

%U 71420983074726546239,3355265920593054081629,157626077284798815290324,7405070366464951264563599,347880681146567910619198829

%N a(n) = Fibonacci(8n+5) mod Fibonacci(8n+1).

%H Vincenzo Librandi, <a href="/A191968/b191968.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (47,-1).

%F G.f.: x*( 29+x ) / ( 1-47*x+x^2 ). - _R. J. Mathar_, Nov 15 2011; adapted to offset by _Bruno Berselli_, Jun 29 2014

%F a(n) = 47*a(n-1) -a(n-2) for n>1. - _Vincenzo Librandi_, Jun 29 2014

%F a(n) = Lucas(8*n - 1) for n >= 1. - _Ehren Metcalfe_, Apr 04 2019

%F a(n) = ((47+21*sqrt(5))^(-n)*(-2^(1+n)*(85+38*sqrt(5)) + (65+29*sqrt(5))*(2207+987*sqrt(5))^n)) / (105+47*sqrt(5)). - _Colin Barker_, Apr 05 2019

%t Table[Mod[Fibonacci[(8*n + 5)] , Fibonacci[(8*n + 1)]], {n, 1, 16}]

%o (Magma) [Fibonacci(8*n+5) mod Fibonacci(8*n+1): n in [1..20]]; // _Vincenzo Librandi_, Jun 29 2014

%o (PARI) a(n)=([0,1; -1,47]^(n-1)*[29;1364])[1,1] \\ _Charles R Greathouse IV_, Jul 06 2017

%o (PARI) Vec(x*(29 + x) / (1 - 47*x + x^2) + O(x^20)) \\ _Colin Barker_, Apr 05 2019

%Y Cf. A000045, A000032.

%K nonn,easy

%O 1,1

%A _Artur Jasinski_, Nov 15 2011