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A171415
a(n) = 99*a(n-1) - a(n-2); a(0) = 0, a(1) = 1.
1
0, 1, 99, 9800, 970101, 96030199, 9506019600, 940999910201, 93149485090299, 9220858024029400, 912771794893820301, 90355186836464180399, 8944250725015060039200, 885390466589654479700401, 87644711941650778430300499, 8675941091756837410120049000, 858830523371985252823454550501
OFFSET
0,3
COMMENTS
Related to Motzkin numbers.
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
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
MATHEMATICA
LinearRecurrence[{99, -1}, {0, 1}, 30] (* Harvey P. Dale, Dec 18 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mark Dols, Dec 08 2009
EXTENSIONS
Offset adapted to definition by Georg Fischer, Jun 18 2021
a(14)-a(16) from Stefano Spezia, Aug 05 2024
STATUS
approved