A191968 a(n) = Fibonacci(8n+5) mod Fibonacci(8n+1).

29, 1364, 64079, 3010349, 141422324, 6643838879, 312119004989, 14662949395604, 688846502588399, 32361122672259149, 1520283919093591604, 71420983074726546239, 3355265920593054081629, 157626077284798815290324, 7405070366464951264563599, 347880681146567910619198829

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (47,-1).

Formula

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

a(n) = 47*a(n-1) -a(n-2) for n>1. - Vincenzo Librandi, Jun 29 2014

a(n) = Lucas(8*n - 1) for n >= 1. - Ehren Metcalfe, Apr 04 2019

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

Mathematica

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

Prog

(Magma) [Fibonacci(8*n+5) mod Fibonacci(8*n+1): n in [1..20]]; // Vincenzo Librandi, Jun 29 2014
(PARI) a(n)=([0, 1; -1, 47]^(n-1)*[29; 1364])[1, 1] \\ Charles R Greathouse IV, Jul 06 2017
(PARI) Vec(x*(29 + x) / (1 - 47*x + x^2) + O(x^20)) \\ Colin Barker, Apr 05 2019

Crossrefs

Cf. A000045, A000032.

Sequence in context: A195740 A139192 A290022 * A049657 A091994 A126555

Adjacent sequences: A191965 A191966 A191967 * A191969 A191970 A191971

Keyword

nonn,easy

Author

Artur Jasinski, Nov 15 2011

Status

approved