A200258 a(n) = Fibonacci(8n+7) mod Fibonacci(8n+1).

32, 1508, 70844, 3328160, 156352676, 7345247612, 345070285088, 16210958151524, 761569962836540, 35777577295165856, 1680784562909958692, 78961096879472892668, 3709490768772315996704, 174267105035419378952420, 8186844445895938494767036

Offset: 1

Author

Artur Jasinski, Nov 15 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..600
• Index entries for linear recurrences with constant coefficients, signature (47,-1).

Programs

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

Mathematica

Table[Mod[Fibonacci[(8 n + 7)] , Fibonacci[(8 n + 1)]], {n, 1, 16}]
CoefficientList[Series[4*(8+x)/(1-47*x+x^2),{x,0,20}],x] (* Vincenzo Librandi, Jul 12 2012 *)

Formula

From Bruno Berselli, Nov 17 2011: (Start)

G.f.: 4*x*(8+x)/(1-47*x+x^2).

a(n) = 47*a(n-1)-a(n-2).

a(n) = ((-5+3r)*(47+21r)^n-(5+3r)*(47-21r)^n)/(5*2^(n-1)) where r=sqrt(5). (End)

a(n) = 32*A049668(n) + 4*A049668(n-1). - R. J. Mathar, Nov 26 2011