[seqfan] Re: guessing doubling formulas for sequences
Robert Israel
israel at math.ubc.ca
Tue Mar 10 22:58:55 CET 2009
On Tue, 10 Mar 2009, Georgi Guninski wrote:
> can someone please give examples of doubling formulas for sequences that
> are not rational (probably exponential)?
For example, a_n = n^n (for n >= 2) has the doubling formula
a_{2n} = a_n^(2+2*ln(2)/LambertW(ln(a_n)))
a_n = n^2 + n + 1 has the doubling formula
a_{2n} = 4 a_n - 2 - sqrt(4 a_n - 3)
Cheers,
Robert Israel
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