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 A154023 a(n+2) = 36*a(n+1) - a(n), a(1)=0, a(2)=6. 1
 0, 6, 216, 7770, 279504, 10054374, 361677960, 13010352186, 468011000736, 16835385674310, 605605873274424, 21784976052204954, 783653532006103920, 28189742176167536166, 1014047064810025198056, 36477504590984739593850 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If a(n)=x and a(n+1)=y then (x^2+y^2)/(xy+1)=36. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..500 Index entries for linear recurrences with constant coefficients, signature (36,-1). FORMULA a(n) = (3/323)*sqrt(323)*( (18+sqrt(323))^(n-1) - (18-sqrt(323))^(n-1) ). - Paolo P. Lava, Jan 15 2009 From R. J. Mathar, Oct 18 2010: (Start) a(n)= +36*a(n-1) -a(n-2) a(n) = 6*A144128(n-1). G.f.: 6*x/(1 -36*x +x^2). (End) MATHEMATICA LinearRecurrence[{36, -1}, {0, 6}, 50] (* Vincenzo Librandi, Jan 30 2012 *) PROG (PARI) concat(0, Vec(6/(1-36*x+x^2)+O(x^98))) \\ Charles R Greathouse IV, Dec 27 2011 CROSSREFS Cf. A065100, A154021-A154027. Sequence in context: A007221 A195802 A145249 * A013711 A300593 A281431 Adjacent sequences:  A154020 A154021 A154022 * A154024 A154025 A154026 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Jan 04 2009 EXTENSIONS Edited by N. J. A. Sloane, Jun 23 2010 at the suggestion of Joerg Arndt. Missing digit inserted in a(8) by R. J. Mathar, Oct 18 2010 STATUS approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)