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A084595
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For n > 0: a(n) = Sum_{r=0..2^(n-1)-1} binomial(2^n, 2r+1)*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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A084594(n)/a(n) converges to sqrt(3). Related to Newton's iteration.
a(n) is divisible by 2^n.
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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*sqrt(3)).
For n > 1:
a(n) = 2*a(n-1)*sqrt(3*a(n-1)^2 + A001146(n-1)).
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MATHEMATICA
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For n>0: Table[Sum[Binomial[2^n, 2 r + 1]3^r, {r, 0, 2^(n - 1) - 1}], {n, 1, 8}]
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PROG
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(PARI) a(n) = if (n==0, 1, sum(r=0, 2^(n-1)-1, binomial(2^n, 2*r+1)*3^r)); \\ Michel Marcus, Sep 09 2019; corrected Jun 13 2022
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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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