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 A075848 2*n^2 + 9 is a square. 5
 0, 6, 36, 210, 1224, 7134, 41580, 242346, 1412496, 8232630, 47983284, 279667074, 1630019160, 9500447886, 55372668156, 322735561050, 1881040698144, 10963508627814, 63900011068740, 372436557784626, 2170719335639016 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Lim. n-> Inf. a(n)/a(n-1) = 3 + 2*Sqrt(2). 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 Harvey P. Dale, Table of n, a(n) for n = 0..1000 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+2*Sqrt(2))^n - (3-2*Sqrt(2))^n] * [3/(2*Sqrt(2))]; a(n) = 6*a(n-1) - a(n-2). a(n) = 6*A001109(n). G.f.: 6x/(1-6x+x^2). [From Philippe Deléham, Nov 17 2008] MATHEMATICA LinearRecurrence[{6, -1}, {0, 6}, 30] (* Harvey P. Dale, Nov 28 2012 *) CROSSREFS Sequence in context: A269406 A269603 A027910 * A096979 A269464 A123887 Adjacent sequences:  A075845 A075846 A075847 * A075849 A075850 A075851 KEYWORD nonn,easy AUTHOR Gregory V. Richardson, Oct 15 2002 STATUS approved

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