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 A158385 676n^2 + 2n. 2
 678, 2708, 6090, 10824, 16910, 24348, 33138, 43280, 54774, 67620, 81818, 97368, 114270, 132524, 152130, 173088, 195398, 219060, 244074, 270440, 298158, 327228, 357650, 389424, 422550, 457028, 492858, 530040, 568574, 608460, 649698, 692288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The identity (676*n+1)^2-(676*n^2+2*n)*(26)^2=1 can be written as A158386(n)^2-a(n)*(26)^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*(26^2*t+2)). Index to sequences with 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*(678+674*x)/(1-x)^3. MATHEMATICA LinearRecurrence[{3, -3, 1}, {678, 2708, 6090}, 50] PROG (MAGMA) I:=[678, 2708, 6090]; [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) = 676*n^2 + 2*n. CROSSREFS Cf. A158386. Sequence in context: A144381 A097773 A031524 * A186127 A097771 A121105 Adjacent sequences:  A158382 A158383 A158384 * A158386 A158387 A158388 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 17 2009 STATUS approved

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