formula

${\rm E}\left[ \sum_{i,j} {\cal R}_i {\cal R}_j \right] &=& 2{\rm E}\left[\sum_{j>i}{\cal R}_i {\cal R}_j \right] {\rm E}\left[ \sum_{i=1}^N{\cal R}_i^2 \right] \\ &=& 2 \sum_{j>i}\mu^{j-i}(\mu^2 \sigma^2)^{N-j 1} \sum_{i=1}^N (\mu^2 \sigma^2)^i$