A171415 a(n) = 99*a(n-1) - a(n-2); a(0) = 0, a(1) = 1.
0, 1, 99, 9800, 970101, 96030199, 9506019600, 940999910201, 93149485090299, 9220858024029400, 912771794893820301, 90355186836464180399, 8944250725015060039200, 885390466589654479700401, 87644711941650778430300499, 8675941091756837410120049000, 858830523371985252823454550501
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (99,-1).
Programs
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Maple
a(0):=0: a(1):=1: for n from 0 to 50 do a(n+2):=99*a(n+1)-a(n): od: seq(a(n),n=0..30); taylor((z/(1-99*z+z^2)),z=0,30); # Richard Choulet, Dec 10 2009
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Mathematica
LinearRecurrence[{99,-1},{0,1},30] (* Harvey P. Dale, Dec 18 2015 *)
Formula
a(n+1)^2 - a(n)^2 = a(2*n+1). - Richard Choulet, Dec 10 2009
G.f.: x/(1-99*x+x^2). - Philippe Deléham, Dec 09 2009
E.g.f.: 2*exp(99*x/2)*sinh(sqrt(9797)*x/2)/sqrt(9797). - Stefano Spezia, Aug 05 2024
Extensions
Offset adapted to definition by Georg Fischer, Jun 18 2021
a(14)-a(16) from Stefano Spezia, Aug 05 2024
Comments