Let $a_1,a_2,\ldots,a_n$ be a finite sequence of non negative integers, its subsequences are the sequences of the form $a_i,a_{i+1},\ldots,a_j$ with $1\le i\le j \le n$. Two subsequences are said to be equal if they have the same length and have the same terms, that is, two subsequences $a_i,a_{i+1},\ldots,a_j$ and $a_u,a_{u+1},\ldots a_v$ are equal iff $j-i=u-v$ and $a_{i+k}=a_{u+k}$ forall integers $k$ such that $0\le k\le j-1$. Finally, we say that a subsequence $a_i,a_{i+1},\ldots,a_j$ is palindromic if $a_{i+k}=a_{j-k}$ forall integers $k$ such that $0\le k \le j-i$ What is the greatest number of different palindromic subsequences that can a palindromic sequence of length $n$ contain?