Let {f(n} be the sequence of integers determined
by the recurrence relation f(n+2) equivalent to 2f(n+1) - f(n) (mod(n+2)) with
f(n) greater than or
equal to 0 and less than n for every integer n greater than or equal to m,
where m is a certain positive integer with initially assigned
arbitrary integers f(m) and f(m+1).
We investigate how the sequence {f(n} increases or decreases.
We call a maximal increasing or decreasing subsequence of consecutive
elements
of the sequence a run. We show that each run is an arithmetic progression and
that the common difference in an increasing run is one more than the common
difference in the previous increasing run, and similary for decreasing runs.