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 A075841 2*k^2 - 9 is a square. 4
 3, 15, 87, 507, 2955, 17223, 100383, 585075, 3410067, 19875327, 115841895, 675176043, 3935214363, 22936110135, 133681446447, 779152568547, 4541233964835, 26468251220463, 154268273357943, 899141388927195 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Lim. n-> Inf. a(n)/a(n-1) = 3 + 2*sqrt(2). Positive values of x (or y) satisfying x^2 - 6*x*y + y^2 + 36 = 0. - Colin Barker, Feb 08 2014 For each member t of the sequence there exists a nonnegative r such that t^2 = r^2 + (r+3)^2. The r values are in A241976. Example: 87^2 = 60^2 + 63^2. - Bruno Berselli, Jul 10 2017 REFERENCES A. H. Beiler, "The Pellian", ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, New York, New York, pp. 248-268, 1966. L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, pp. 341-400. Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, pp. 139-147. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Tanya Khovanova, Recursive Sequences J. J. O'Connor and E. F. Robertson, Pell's Equation Eric Weisstein's World of Mathematics, Pell Equation. Index entries for linear recurrences with constant coefficients, signature (6,-1). FORMULA a(n) = 3*sqrt(2)/4*((1+sqrt(2))^(2*n-1)-(1-sqrt(2))^(2*n-1)) = 6*a(n-1) - a(n-2). G.f.: 3*x*(1-x)/(1-6*x+x^2). - Philippe Deléham, Nov 17 2008 a(n) = 3*A001653(n). - R. J. Mathar, Sep 27 2014 MATHEMATICA CoefficientList[Series[3 (1 - x)/(1 - 6 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 11 2014 *) PROG (PARI) isok(n) = issquare(2*n^2-9); \\ Michel Marcus, Jul 10 2017 CROSSREFS Sequence in context: A001931 A180677 A220875 * A152596 A278392 A168503 Adjacent sequences:  A075838 A075839 A075840 * A075842 A075843 A075844 KEYWORD nonn,easy AUTHOR Gregory V. Richardson, Oct 14 2002 STATUS approved

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