Special Undergraduate Lecture
Thursday, April 17, 6:30-8:00 pm in BLOCKER 113.
Pizza and soda will be available at 6:30, the talk will start at 7:00 pm.
PROFESSOR BRUCE REZNICK (University of Illinois)
EXPLORING THE STERN SEQUENCE
The Stern Sequence is defined by the recurrence
s(0) = 0,
s(1) = 1
and
s(2n) = s(n) and
s(2n + 1) = s(n) + s(n + 1).
The first 16 terms are
0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1.
By writing the terms from 2 to 2r+1 in the r-th row, it can be visualized as a kind of Pascal’s
triangle with memory.
r
The Stern sequence has more properties than the Fibonacci sequence. (In fact, the maximum values
in each row are consecutive Fibonacci numbers.) In this talk, I will present the Stern sequence and
invite the audience to make its observations and suggestions about potential properties. This will
guide the discussion, since there’s enough here to fill an entire graduate course!
There are no specific requirements for this talk, beyond the ability to add integers. It will help if
you know a little number theory and a little combinatorics, but these will be developed as needed. It
will really help if you are willing to make conjectures and guess based on the data provided. Please
keep in mind that the speaker does not know your name and will never be giving you a grade in a
class.