Search: id:A157912
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%I A157912
%S A157912 80,272,592,1040,1616,2320,3152,4112,5200,6416,7760,9232,10832,12560,
%T A157912 14416,16400,18512,20752,23120,25616,28240,30992,33872,36880,40016,
%U A157912 43280,46672,50192,53840,57616,61520,65552,69712,74000,78416,82960
%N A157912 a(n)=64*n^2+16 (n>0)
%C A157912 If A=[A157912] 64*n.^2+16 (80, 272, 592,.,); Y=[A000027] n (1, 2,4,6,
               8,.,); X=[A081585] 8*n^2 + 1 (n>0, 9, 33, 73..,), we have, for all 
               terms, Pell's equation X^2-A*Y^2=1. Example: 9^2-80 *1\^2=1; 33^2-272*2^2=1; 
               73^2-592*3^2=1.
%H A157912 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 A157912 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%H A157912 Philippe Chevanne, <a href="http://mathafou.free.fr/themes/kpell.html">
               Pell Equation</a>
%F A157912 a(n)=64*n^2+16 (n>0)
%e A157912 For n=1, a(1)=80; n=2, a(2)=272; n=3, a(3)=592
%Y A157912 Cf. A000027, A081585
%Y A157912 Sequence in context: A044712 A044412 A044793 this_sequence A057441 A157953 
               A045666
%Y A157912 Adjacent sequences: A157909 A157910 A157911 this_sequence A157913 A157914 
               A157915
%K A157912 nonn
%O A157912 1,1
%A A157912 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 09 2009

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