Search: id:A158742
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%I A158742
%S A158742 1,75,297,667,1185,1851,2665,3627,4737,5995,7401,8955,10657,12507,14505,
%T A158742 16651,18945,21387,23977,26715,29601,32635,35817,39147,42625,46251,
%U A158742 50025,53947,58017,62235,66601,71115,75777,80587,85545,90651,95905
%N A158742 a(n)=74*n^2+1.
%C A158742 The identity (74*n^2+1)^2 - (1369*n^2+37) * (2*n)^2 = 1 can be written 
               as
%C A158742 the Pell equation (a(n))^2 - A158741(n) * (A005843(n))^2 = 1.
%H A158742 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html"> 
               Pell Equation</a>
%H A158742 Edward Everett Withford, <a href="http://quod.lib.umich.edu/cgi/t/text/
               text-idx?c=umhistmath;cc=umhistmath;idno=abv2773.0001.001;view=toc"> 
               Pell Equation</a>
%H A158742 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%F A158742 a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: -(1+72*x+75*x^2)/(x-1)^3.
%Y A158742 Cf. A005843, A158741
%Y A158742 Sequence in context: A044788 A003503 A098230 this_sequence A158765 A055561 
               A015223
%Y A158742 Adjacent sequences: A158739 A158740 A158741 this_sequence A158743 A158744 
               A158745
%K A158742 nonn,easy
%O A158742 0,2
%A A158742 Vincenzo Librandi (vincenzo.librandi(AT)tn.it), Mar 25 2009
%E A158742 Comment rewritten, a(0) added and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), 
               Oct 22 2009

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