%I A051009
%S A051009 1,2,12,408,470832,627013566048,1111984844349868137938112,
%T A051009 3497379255757941172020851852070562919437964212608
%N A051009 Reduced denominators of Newton's iteration for sqrt(2).
%C A051009 For n>=4, A051009(n) = A098890(n-2) - A098890(n-3) - Kieren MacMillan 
               (kieren(AT)alumni.rice.edu), Dec 19 2007
%C A051009 (2^n)-th Pell numbers [From Sergio Falcon (sfalcon(AT)dma.ulpgc.es), 
               Dec 04 2008]
%H A051009 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NewtonsIteration.html">Link to a section of The World of Mathematics.</
               a>
%H A051009 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SquareRoot.html">Link to a section of The World of Mathematics.</
               a>
%H A051009 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PythagorassConstant.html">Pythagoras's Constant</a>
%F A051009 a(n) = 2*a(n-1)*A001601(n-1) - Joe Keane (jgk(AT)jgk.org), May 31 2002
%F A051009 sqrt(2) = 1 + 1/2 - sum_{n=3, infinity} (1/a(n)). - Donald S. McDonald 
               (don.mcdonald(AT)paradise.net.nz), Jan 21 2003
%F A051009 For n>1: a(n)=2a(n-1)*sqrt(2a(n-1)^2+1). - Mario Catalani (mario.catalani(AT)unito.it), 
               May 27 2003
%F A051009 For n>0: a(n)=sum(binomial[2^n, 2r+1]2^r, r=0, .., 2^(n-1)-1) - Mario 
               Catalani (mario.catalani(AT)unito.it), May 30 2003
%F A051009 a(n)=(1/(2 Sqrt[2])) ((1 + Sqrt[2])^(2^n) - (1 - Sqrt[2])^(2^n))]], {n, 
               0, 7}] [From Artur Jasinski (grafix(AT)csl.pl), Oct 10 2008]
%t A051009 Table[Simplify[Expand[(1/(2 Sqrt[2])) ((1 + Sqrt[2])^(2^n) - (1 - Sqrt[2])^(2^n))]], 
               {n, 0, 7}] [From Artur Jasinski (grafix(AT)csl.pl), Oct 10 2008]
%t A051009 Do[Print[Fibonacci[2^n,2]],{n,0,10}] [From Sergio Falcon (sfalcon(AT)dma.ulpgc.es), 
               Dec 04 2008]
%Y A051009 Cf. A001601.
%Y A051009 a(n) = A000129(2^n).
%Y A051009 Cf. A098890.
%Y A051009 A000129 [From Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Dec 04 2008]
%Y A051009 Sequence in context: A009706 A012551 A156509 this_sequence A060942 A072446 
               A015181
%Y A051009 Adjacent sequences: A051006 A051007 A051008 this_sequence A051010 A051011 
               A051012
%K A051009 nonn,frac
%O A051009 1,2
%A A051009 Eric Weisstein (eric(AT)weisstein.com)