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 A075835 Numbers n such that 13*n^2 + 4 is a square. 1
 0, 3, 33, 360, 3927, 42837, 467280, 5097243, 55602393, 606529080, 6616217487, 72171863277, 787274278560, 8587845200883, 93679022931153, 1021881407041800, 11147016454528647, 121595299592773317 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Lim. n-> Inf. a(n)/a(n-1) = (11 + Sqrt(13))/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. S. Falcon, Relationships between Some k-Fibonacci Sequences, Applied Mathematics, 2014, 5, 2226-2234; http://www.scirp.org/journal/am; http://dx.doi.org/10.4236/am.2014.515216 LINKS 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 (11,-1). FORMULA a(n) = [(11 + 3*Sqrt(13))^n - (11 - 3*Sqrt(13))^n] / [(2^n) * Sqrt(13)] a(n) = 11*a(n-1)-a(n-2)with a(1)=0 and a(2)=3. G.f.: 3x^2/(1-11x+x^2). [From Philippe Deléham, Nov 17 2008] a(n) = A006190(2*n). - Vladimir Reshetnikov, Sep 16 2016 MATHEMATICA LinearRecurrence[{11, -1}, {0, 3}, 20] (* Harvey P. Dale, Dec 27 2011 *) Table[Fibonacci[2n, 3], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *) CROSSREFS Cf. A006190. Sequence in context: A001507 A221162 A231594 * A077698 A080488 A082778 Adjacent sequences:  A075832 A075833 A075834 * A075836 A075837 A075838 KEYWORD nonn,easy AUTHOR Gregory V. Richardson, Oct 14 2002 STATUS approved

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Last modified June 24 09:55 EDT 2019. Contains 324323 sequences. (Running on oeis4.)