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

Offset

0,3

Comments

Related to Motzkin numbers.

Links

Table of n, a(n) for n=0..13.

Index entries for linear recurrences with constant coefficients, signature (99,-1).

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

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

Cf. A168520, A168522, A004189.

Sequence in context: A213155 A046173 A278620 * A327926 A098609 A195623

Adjacent sequences: A171412 A171413 A171414 * A171416 A171417 A171418

Keyword

nonn,easy

Author

Mark Dols, Dec 08 2009

Extensions

Offset adapted to definition by Georg Fischer, Jun 18 2021

Status

approved