Search: id:A158765
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%I A158765
%S A158765 75,303,683,1215,1899,2735,3723,4863,6155,7599,9195,10943,12843,14895,
%T A158765 17099,19455,21963,24623,27435,30399,33515,36783,40203,43775,47499,
%U A158765 51375,55403,59583,63915,68399,73035,77823,82763,87855,93099,98495
%N A158765 a(n)=76*n^2-1.
%C A158765 The identity (76*n^2-1)^2 - (1444*n^2-38) * (2*n)^2 = 1 can be written 
               as
%C A158765 the Pell equation (a(n))^2 - A158764(n) * (A005843(n))^2 = 1.
%H A158765 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html"> 
               Pell Equation</a>
%H A158765 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0"> 
               X^2-AY^2=1</a>
%H A158765 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>
%F A158765 a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: x*(-75-78*x+x^2)/(x-1)^3.
%Y A158765 Cf. A005843, A158764
%Y A158765 Sequence in context: A003503 A098230 A158742 this_sequence A055561 A015223 
               A129625
%Y A158765 Adjacent sequences: A158762 A158763 A158764 this_sequence A158766 A158767 
               A158768
%K A158765 nonn,easy
%O A158765 1,1
%A A158765 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 26 2009
%E A158765 Comment rewritten and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), 
               Oct 22 2009

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