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 A157666 a(n) = 19683*n - 13716. 3
 5967, 25650, 45333, 65016, 84699, 104382, 124065, 143748, 163431, 183114, 202797, 222480, 242163, 261846, 281529, 301212, 320895, 340578, 360261, 379944, 399627, 419310, 438993, 458676, 478359, 498042, 517725, 537408, 557091, 576774, 596457 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The identity (531441*n^2 - 740664*n + 258065)^2 - (729*n^2 - 1016*n + 354)*(19683*n - 13716)^2 = 1 can be written as A157667(n)^2 - A157665(n)*a(n)^2 = 1. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Vincenzo Librandi, X^2-AY^2=1 Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA From Harvey P. Dale, Nov 03 2011: (Start) G.f.: 27*x*(508*x+221)/(x-1)^2. a(n) = 2*a(n-1) - a(n-2); a(1)=5967, a(2)=25650. (End) E.g.f.: 27*(508 - (508 - 729*x)*exp(x)). - G. C. Greubel, Nov 17 2018 EXAMPLE a(1) = 19683*1 - 13716 = 5967; a(2) = 19683*2 - 13716 = 25650. MATHEMATICA 19683Range[40]-13716 (* or *) LinearRecurrence[{2, -1}, {5967, 25650}, 40] (* Harvey P. Dale, Nov 03 2011 *) PROG (Magma) I:=[5967, 25650]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; (PARI) a(n) = 19683*n - 13716. (Sage) [19683*n-13716 for n in (1..40)] # G. C. Greubel, Nov 17 2018 (GAP) List([1..40], n -> 19683*n-13716); # G. C. Greubel, Nov 17 2018 CROSSREFS Cf. A157665, A157667. Sequence in context: A186479 A266038 A032658 * A176374 A282191 A328327 Adjacent sequences: A157663 A157664 A157665 * A157667 A157668 A157669 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 04 2009 EXTENSIONS Example edited by Jon E. Schoenfield, Nov 17 2018 STATUS approved

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Last modified December 3 11:24 EST 2022. Contains 358517 sequences. (Running on oeis4.)