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%I #31 Aug 05 2024 10:30:06
%S 0,1,99,9800,970101,96030199,9506019600,940999910201,93149485090299,
%T 9220858024029400,912771794893820301,90355186836464180399,
%U 8944250725015060039200,885390466589654479700401,87644711941650778430300499,8675941091756837410120049000,858830523371985252823454550501
%N a(n) = 99*a(n-1) - a(n-2); a(0) = 0, a(1) = 1.
%C Related to Motzkin numbers.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (99,-1).
%F a(n+1)^2 - a(n)^2 = a(2*n+1). - _Richard Choulet_, Dec 10 2009
%F G.f.: x/(1-99*x+x^2). - _Philippe Deléham_, Dec 09 2009
%F E.g.f.: 2*exp(99*x/2)*sinh(sqrt(9797)*x/2)/sqrt(9797). - _Stefano Spezia_, Aug 05 2024
%p 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);
%p taylor((z/(1-99*z+z^2)),z=0,30); # _Richard Choulet_, Dec 10 2009
%t LinearRecurrence[{99,-1},{0,1},30] (* _Harvey P. Dale_, Dec 18 2015 *)
%Y Cf. A168520, A168522, A004189.
%K nonn,easy
%O 0,3
%A _Mark Dols_, Dec 08 2009
%E Offset adapted to definition by _Georg Fischer_, Jun 18 2021
%E a(14)-a(16) from _Stefano Spezia_, Aug 05 2024