A154027 a(n+2) = 100*a(n+1) - a(n), a(1)=0, a(2)=10.

0, 10, 1000, 99990, 9998000, 999700010, 99960003000, 9995000599990, 999400099996000, 99930014999000010, 9992002099800005000, 999100279965001499990, 99900035994400349994000, 9989004499160069997900010

Offset: 1

Author

Vincenzo Librandi, Jan 04 2009

Keywords

• nonn
• easy

Comments

If a(n)=x and a(n+1)=y then (x^2+y^2)/(xy+1)=100.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (100,-1).

Crossrefs

Cf. A065100, A154021-A154026.

Programs

Magma

I:=[0, 10]; [n le 2 select I[n] else 100*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Feb 26 2012

Mathematica

LinearRecurrence[{100,-1},{0,10},20] (* Vincenzo Librandi, Feb 26 2012 *)
CoefficientList[Series[(10*x)/(1-100*x+x^2),{x,0,20}],x] (* Harvey P. Dale, Aug 15 2012 *)

PARI

a(n)=([0,1;-1,100]^n*[0;10])[1,1] \\ Charles R Greathouse IV, Sep 01 2016

Formula

G.f.: (10*x)/(1 -100*x +x^2). - Harvey P. Dale, Aug 15 2012