Let [unparseable or potentially dangerous latex formula] be an integer. Find, with proof, all sequences [unparseable or potentially dangerous latex formula] of positive integers with the following three properties:
a) [unparseable or potentially dangerous latex formula]
b) x_i+x_{n-i}=2n for all [unparseable or potentially dangerous latex formula]
c) given any two indices [unparseable or potentially dangerous latex formula] (not necessarily distinct) for which [unparseable or potentially dangerous latex formula], there is an index [unparseable or potentially dangerous latex formula] such that [unparseable or potentially dangerous latex formula]