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Math 192r, Problem Set \#14 \\
(due 11/13/01)
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\begin{enumerate}
\item
Use the recurrence for $p(n)$
to compute the last digit of $p(n)$
for every $n$ between 1 and 1000.
Can you make any conjectures about the relationship
between the last digit of $n$
and the last digit of $p(n)$?
\item
Let $F(0)=1$
and recursively define
$F(n)=F(n-1)+F(n-3)-F(n-6)-F(n-10)+F(n-15)+F(n-21)--++...$
for all $n>0$,
where terms of the form $F(n-k)$ are to be ignored
once $k \geq n$.
There exists a set $S$ of positive integers such that
$F(n)$ equals the number of partitions of $n$
into parts belonging to $S$.
Find $S$ (conjecturally).
\end{enumerate}
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