Intended for: January 5, 2012
Timetable
- First draft entered by Alonso del Arte on November 3, 2011 ✓
- Draft to be reviewed by November 5, 2011
- Draft to be approved by December 5, 2011
Yesterday's SOTD * Tomorrow's SOTD
The line below marks the end of the <noinclude> ... </noinclude> section.
A000081: Number of
rooted trees with
nodes (or connected functions with a fixed point).
-
{ 1, 1, 2, 4, 9, 20, 48, 115, ... }
My interest in this sequence today has to do not with trees or anything in graph theory, but with the following number-theoretical problem:
Given
instances of some constant
with
exponentiation carets and parentheses inserted in every valid way, how many distinct values are produced by the resulting expressions? The answer depends on what
is. With four instances of
, there are four distinct values, but with four instances of
(the
imaginary unit), only three distinct values are produced.
But what if you don’t know what
is? Is there an upper bound for
instances of
? This sequence is the answer.