Search: id:A158537
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%I A158537
%S A158537 1,23,89,199,353,551,793,1079,1409,1783,2201,2663,3169,3719,4313,4951,
%T A158537 5633,6359,7129,7943,8801,9703,10649,11639,12673,13751,14873,16039,
%U A158537 17249,18503,19801,21143,22529,23959,25433,26951,28513,30119,31769
%N A158537 22*n^2+1.
%C A158537 From the Pell-type identity (22*n^2+1)^2 - (121*n^2+11) * (2*n)^2 = 1 
               we derive
%C A158537 (a(n))^2 - A158536(n) * (A005843(n))^2 = 1.
%H A158537 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0"> 
               X^2-AY^2=1</a>
%H A158537 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%H A158537 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 A158537 a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: (1+20*x+23*x^2)/(1-x)^3.
%Y A158537 Cf. A005843, A158536
%Y A158537 Sequence in context: A044591 A050255 A014088 this_sequence A117049 A142062 
               A050529
%Y A158537 Adjacent sequences: A158534 A158535 A158536 this_sequence A158538 A158539 
               A158540
%K A158537 nonn,easy
%O A158537 0,2
%A A158537 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 21 2009
%E A158537 Comment rewritten, a(0) added - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 16 2009

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