Search: id:A060656
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%I A060656
%S A060656 1,1,2,4,16,64,512,4096,65536,1048576,33554432,1073741824,68719476736,
%T A060656 4398046511104,562949953421312,72057594037927936,18446744073709551616,
%U A060656 4722366482869645213696,2417851639229258349412352
%N A060656 a(n)=2a(n-1)*a(n-2)/a(n-3) with a(0)=a(1)=1.
%C A060656 a(n+1) is the Hankel transform of A135052. - Paul Barry (pbarry(AT)wit.ie), 
               Nov 15 2007
%C A060656 Contribution from Paul Barry (pbarry(AT)wit.ie), Dec 08 2009: (Start)
%C A060656 a(n+1) is the Hankel transform of the aerated large Schroeder numbers. 
               a(n) and a(n+1) both satisfy the trivial
%C A060656 Somos-4 recurrence u(n)=4*u(n-2)^2/u(n-4). Associated to elliptic curve 
               y^2=1-6x^2+x^4 via Schroeder numbers. (End)
%H A060656 Harry J. Smith, <a href="b060656.txt">Table of n, a(n) for n=0,...,100</
               a>
%F A060656 a(n) =2^[ n^2/4 ] =a(n-1)*2^[ n/2 ] =a(n-2)*2^(n-1) =a(n-1)*A016116(n) 
               =2^A002620(n).
%e A060656 a(6)=2*64*16/4=512.
%o A060656 (PARI) { for (n=0, 100, write("b060656.txt", n, " ", 2^(n^2\4)); ) } 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 09 2009]
%Y A060656 Cf. A038754.
%Y A060656 Cf. A002416.
%Y A060656 Sequence in context: A153998 A154001 A154004 this_sequence A061286 A019279 
               A061652
%Y A060656 Adjacent sequences: A060653 A060654 A060655 this_sequence A060657 A060658 
               A060659
%K A060656 easy,nonn,new
%O A060656 0,3
%A A060656 Henry Bottomley (se16(AT)btinternet.com), Apr 18 2001

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