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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Related to Motzkin numbers LINKS Index entries for linear recurrences with constant coefficients, signature (99,-1). FORMULA a(n)= (1/sqrt(9797))*((99+sqrt(9797)/2)^n-(1/sqrt(9797))*((99-sqrt(9797)/2)^n. a(n+1)^2-a(n)^2=a(2*n+1). [From Richard Choulet, Dec 10 2009] G.f.: x/(1-99*x+x^2). [From Philippe Deléham, Dec 09 2009] a(n)=(1/9797)*sqrt(9797)*{[(99/2)+(1/2)*sqrt(9797)]^n-[(99/2)-(1/2)*sqrt(9797)]^n}, with n>=0 [From Paolo P. Lava, Dec 14 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); [From 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 * A098609 A195623 A274743 Adjacent sequences:  A171412 A171413 A171414 * A171416 A171417 A171418 KEYWORD nonn,easy AUTHOR Mark Dols, Dec 08 2009 STATUS approved

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Last modified March 19 15:02 EDT 2019. Contains 321330 sequences. (Running on oeis4.)