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A060656
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a(n)=2a(n-1)*a(n-2)/a(n-3) with a(0)=a(1)=1.
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6
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1, 1, 2, 4, 16, 64, 512, 4096, 65536, 1048576, 33554432, 1073741824, 68719476736, 4398046511104, 562949953421312, 72057594037927936, 18446744073709551616, 4722366482869645213696, 2417851639229258349412352
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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a(n+1) is the Hankel transform of A135052. - Paul Barry, Nov 15 2007
Contribution from Paul Barry, Dec 08 2009: (Start)
a(n+1) is the Hankel transform of the aerated large Schroeder numbers. a(n) and a(n+1) both satisfy the trivial
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)
Hankel transform of A089324. [From Paul Barry, Mar 01 2010]
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,100
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FORMULA
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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).
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EXAMPLE
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a(6)=2*64*16/4=512.
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PROG
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(PARI) { for (n=0, 100, write("b060656.txt", n, " ", 2^(n^2\4)); ) } [From Harry J. Smith, Jul 09 2009]
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CROSSREFS
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Cf. A038754.
Cf. A002416.
Sequence in context: A153998 A154001 A154004 * A061286 A019279 A061652
Adjacent sequences: A060653 A060654 A060655 * A060657 A060658 A060659
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley, Apr 18 2001
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STATUS
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approved
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