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A084594
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a(n) = Sum_{r=0..2^(n-1)} Binomial(2^n,2r)*3^r.
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1
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OFFSET
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0,2
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COMMENTS
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a(n)/A084595(n) converges to sqrt(3). Related to Newton's iteration.
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LINKS
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FORMULA
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a(n) = ( (1+sqrt(3))^(2^n) + (1-sqrt(3))^(2^n) )/2.
a(n) = 2*a(n-1)^2 - A001146(n-1), n>1.
a(n) = a(n-1)^2 + 3*A084595(n-1)^2.
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MATHEMATICA
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Table[Sum[Binomial[2^n, 2 r]3^r, {r, 0, 2^(n - 1)}], {n, 0, 8}]
Table[Simplify[Expand[(1/2) ((1 + Sqrt[3])^(2^n) + (1 - Sqrt[3])^(2^n))]], {n, 0, 7}] (* Artur Jasinski, Oct 11 2008 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), May 31 2003
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STATUS
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approved
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