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# Template:Sequence of the Day for February 2

Intended for: February 2, 2012

## Timetable

• First draft entered by Alonso del Arte on November 3, 2011
• Draft reviewed by Daniel Forgues on January 29, 2017 ✓ (presentation review only)
• Draft to be approved by January 2, 2012

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A196244: Number of distinct values taken by
 r  r  ⋰  r
where
r =
 1 2
(with
 n
 r
’s and parentheses inserted in all possible ways).
{ 1, 1, 2, 4, 9, 20, 47, ... }
In the case of say,
 n = 4
, we’re considering the expressions
${\displaystyle {\begin{array}{l}\displaystyle {{\frac {1}{2}}^{\left({\frac {1}{2}}^{\left({\frac {1}{2}}^{\frac {1}{2}}\right)}\right)},}\end{array}}}$${\displaystyle {\begin{array}{l}\displaystyle {{\frac {1}{2}}^{\left({\left({\frac {1}{2}}^{\frac {1}{2}}\right)}^{\frac {1}{2}}\right)},}\end{array}}}$${\displaystyle {\begin{array}{l}\displaystyle {{\left({\frac {1}{2}}^{\frac {1}{2}}\right)}^{\left({\frac {1}{2}}^{\frac {1}{2}}\right)},}\end{array}}}$${\displaystyle {\begin{array}{l}\displaystyle {{\left({\frac {1}{2}}^{\left({\frac {1}{2}}^{\frac {1}{2}}\right)}\right)}^{\frac {1}{2}},}\end{array}}}$${\displaystyle {\begin{array}{l}\displaystyle {{\left({\left({\frac {1}{2}}^{\frac {1}{2}}\right)}^{\frac {1}{2}}\right)}^{\frac {1}{2}},}\end{array}}}$

and whether or not these expressions result in distinct values or not.