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 A158394 729n^2 - 2n. 2
 727, 2912, 6555, 11656, 18215, 26232, 35707, 46640, 59031, 72880, 88187, 104952, 123175, 142856, 163995, 186592, 210647, 236160, 263131, 291560, 321447, 352792, 385595, 419856, 455575, 492752, 531387, 571480, 613031, 656040, 700507, 746432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The identity (729*n-1)^2-(729*n^2-2*n)*(27)^2=1 can be written as A158395(n)^2-a(n)*(27)^2=1. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..10000 Vincenzo Librandi, X^2-AY^2=1 E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(27^2*t-2)). Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: x*(-727-731*x)/(x-1)^3. MATHEMATICA LinearRecurrence[{3, -3, 1}, {727, 2912, 6555}, 50] PROG (MAGMA) I:=[727, 2912, 6555]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; (PARI) a(n) = 729*n^2 - 2*n. CROSSREFS Cf. A158395. Sequence in context: A103170 A153215 A129117 * A038600 A157430 A215158 Adjacent sequences:  A158391 A158392 A158393 * A158395 A158396 A158397 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 18 2009 STATUS approved

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Last modified January 18 19:50 EST 2020. Contains 331030 sequences. (Running on oeis4.)