%I A075869
%S A075869 3,51,915,16419,294627,5286867,94868979,1702354755,30547516611,
%T A075869 548152944243,9836205479763,176503545691491,3167227616967075,
%U A075869 56833593559715859,1019837456457918387,18300240622682815107
%N A075869 5*n^2 - 9 is a square.
%C A075869 Lim. n-> Inf. a(n)/a(n-1) = phi^6 = 9 + 4*Sqrt(5).
%D A075869 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.
%D A075869 L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine 
               Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, 
               p. 341-400.
%D A075869 Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics 
               Source Series, V. 16); American Mathematical Society, Providence, 
               Rhode Island, 1999, p. 139-147.
%H A075869 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A075869 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A075869 J. J. O'Connor and E. F. Robertson, <a href="http://www-gap.dcs.st-and.ac.uk/
               ~history/HistTopics/Pell.html">Pell's Equation</a>
%H A075869 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PellEquation.html">Link to a section of The World of Mathematics.</
               a>
%F A075869 a(n) = 3*sqrt(5)/10*((2+sqrt(5))^(2*n-1)-(2-sqrt(5))^(2*n-1)) = 18*a(n-1) 
               - a(n-2)
%F A075869 G.f.: 3x*(1-3x)/(1-18x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 17 2008]
%Y A075869 Cf. 3*A007805.
%Y A075869 Sequence in context: A062216 A045489 A145242 this_sequence A126685 A105639 
               A003028
%Y A075869 Adjacent sequences: A075866 A075867 A075868 this_sequence A075870 A075871 
               A075872
%K A075869 nonn
%O A075869 1,1
%A A075869 Gregory V. Richardson (omomom(AT)hotmail.com), Oct 16 2002