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A154027
a(n+2) = 100*a(n+1) - a(n), a(1)=0, a(2)=10.
7
0, 10, 1000, 99990, 9998000, 999700010, 99960003000, 9995000599990, 999400099996000, 99930014999000010, 9992002099800005000, 999100279965001499990, 99900035994400349994000, 9989004499160069997900010
OFFSET
1,2
COMMENTS
If a(n)=x and a(n+1)=y then (x^2+y^2)/(xy+1)=100.
FORMULA
G.f.: (10*x)/(1 -100*x +x^2). - Harvey P. Dale, Aug 15 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 *)
PROG
(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
(PARI) a(n)=([0, 1; -1, 100]^n*[0; 10])[1, 1] \\ Charles R Greathouse IV, Sep 01 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 04 2009
STATUS
approved