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 A158367 529n^2 + 2n. 2
 531, 2120, 4767, 8472, 13235, 19056, 25935, 33872, 42867, 52920, 64031, 76200, 89427, 103712, 119055, 135456, 152915, 171432, 191007, 211640, 233331, 256080, 279887, 304752, 330675, 357656, 385695, 414792, 444947, 476160, 508431, 541760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The identity (529*n+1)^2-(529*n^2+2*n)*(23)^2=1 can be written as A158368(n)^2-a(n)*(23)^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*(23^2*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*(531+527*x)/(1-x)^3. MATHEMATICA LinearRecurrence[{3, -3, 1}, {531, 2120, 4767}, 50] PROG (Magma) I:=[531, 2120, 4767]; [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) = 529*n^2 + 2*n. CROSSREFS Cf. A158368. Sequence in context: A031521 A156772 A031701 * A225937 A225936 A098257 Adjacent sequences: A158364 A158365 A158366 * A158368 A158369 A158370 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 17 2009 STATUS approved

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Last modified September 19 02:20 EDT 2024. Contains 376003 sequences. (Running on oeis4.)