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 A154254 a(n) = 9n^2 - 8n + 2. 4
 2, 3, 22, 59, 114, 187, 278, 387, 514, 659, 822, 1003, 1202, 1419, 1654, 1907, 2178, 2467, 2774, 3099, 3442, 3803, 4182, 4579, 4994, 5427, 5878, 6347, 6834, 7339, 7862, 8403, 8962, 9539, 10134, 10747, 11378, 12027, 12694, 13379, 14082, 14803, 15542 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The identity (81*n^2 + 90*n + 26)^2 - (9*n^2 + 10*n + 3)*(27*n + 15)^2 = 1 can be written as A154277(n+1)^2 - a(n+1)*A154267(n)^2 = 1. - Vincenzo Librandi, Feb 03 2012 For n >= 1, the continued fraction expansion of sqrt(a(n)) is [3n-2; {1, 2, 3n-2, 2, 1, 6n-4}]. For n=1, this collapses to [1; {1, 2}]. - Magus K. Chu, Sep 09 2022 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Vincenzo Librandi, Jan 30 2012: (Start) G.f.: (2 - 3*x + 19*x^2)/(1-x)^3. a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). (End) MATHEMATICA LinearRecurrence[{3, -3, 1}, {2, 3, 22}, 50] (* Vincenzo Librandi, Jan 30 2012 *) PROG (PARI) a(n)=9*n^2-8*n+2 \\ Charles R Greathouse IV, Dec 27 2011 (Magma) I:=[2, 3, 22]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012 CROSSREFS Cf. A154267, A154277. Sequence in context: A298470 A083178 A268866 * A264696 A166122 A366405 Adjacent sequences: A154251 A154252 A154253 * A154255 A154256 A154257 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Jan 05 2009 EXTENSIONS 7662 replaced by 7862 by R. J. Mathar, Jan 07 2009 Edited by Charles R Greathouse IV, Jul 25 2010 STATUS approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)