A168520 a(n) = 98*a(n-1) - a(n-2); a(1) = 0, a(2) = 10.
0, 10, 980, 96030, 9409960, 922080050, 90354434940, 8853812544070, 867583274883920, 85014307126080090, 8330534515080964900, 816307368170808480110, 79989791546224150085880, 7838183264161795899936130, 768061970096309774043654860, 75262234886174196060378240150
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..503
- Index entries for linear recurrences with constant coefficients, signature (98, -1).
Programs
-
Magma
I:=[0,10]; [n le 2 select I[n] else 98*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Oct 13 2015
-
Mathematica
LinearRecurrence[{98,-1},{0,10},30] (* Harvey P. Dale, Sep 19 2011 *) CoefficientList[Series[10 x/(x^2 - 98 x + 1), {x, 0, 33}], x] (* Vincenzo Librandi, Oct 13 2015 *) -
PARI
concat(0, Vec(10*x^2/(x^2-98*x+1) + O(x^30))) \\ Colin Barker, Oct 08 2015
Formula
From Colin Barker, Oct 08 2015: (Start)
a(n) = 98*a(n-1) - a(n-2) for n>2.
O.g.f.: 10*x^2 / (x^2-98*x+1). (End)
E.g.f.: exp(49*x)*( (49/(2*sqrt(6)))*sinh(20*sqrt(6)*x) - 10*cosh(20*sqrt(6)*x) ) + 10. - G. C. Greubel, Jul 24 2016
Extensions
a(1)=1 changed to a(1)=10, and data changed accordingly, so sequence is a bisection of A004189- Mark Dols, Feb 01 2010
Changed name to match data and offset, Joerg Arndt, Oct 13 2015