Search: id:A158443
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%I A158443
%S A158443 12,60,140,252,396,572,780,1020,1292,1596,1932,2300,2700,3132,3596,4092,
%T A158443 4620,5180,5772,6396,7052,7740,8460,9212,9996,10812,11660,12540,13452,
%U A158443 14396,15372,16380,17420,18492,19596,20732,21900,23100,24332,25596
%N A158443 a(n)=16*n^2-4 (n>0)
%C A158443 If A=[A158443] 16*n.^2-4 (n>0, 12, 60,140,.,); Y=[A005843] 2*n (n>0, 
               2, 4, 6,.,); X=[A157914] 8*n^2-1 (n>0, 7, 31, 71, .,), we have, for 
               all terms, Pell's equation X^2-A*Y^2=1. Example: 7^2-12*2^2=1; 31^2-60*4^2=1; 
               71^2-140*6^2=1.
%H A158443 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 A158443 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%H A158443 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%F A158443 a(n)=16*n^2-4 (n>0)
%e A158443 For n=1, a(1)=12; n=2, a(2)=60; n=3, a(3)=140
%Y A158443 Cf. A157914, A005843
%Y A158443 Sequence in context: A120644 A099829 A099830 this_sequence A153792 A000141 
               A008530
%Y A158443 Adjacent sequences: A158440 A158441 A158442 this_sequence A158444 A158445 
               A158446
%K A158443 nonn
%O A158443 1,1
%A A158443 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 19 2009

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