I am dealing with a portfolio allocation problem, but my question is primarily about mathematical notation. I apologize in advance if this is not the correct Stack Exchange but I think this question belongs here more than Stats or even Quant.
Suppose I have four currencies: USD, GBP, EUR and YEN. Therefore, I have six possible returns: USD/GBP, USD/EUR, USD/YEN, GBP/EUR, GBP/YEN and EUR/YEN. I am calling "c" the number of currencies and "n" the number of returns, so: $n=\frac{c(c-1)}{2}$. If I have a portfolio with these four currencies, it makes no sense to calculate the return of, say, YEN/USD, if I have already accounted for USD/YEN.
Now I want to generalize for any currency. I am calling them currency 1, currency 2, currency 3, currency 4. Again, I have six possible returns, which I am going to denote by $R_{12}$, $R_{13}$, $R_{14}$, $R_{23}$, $R_{24}$, $R_{34}$.
My objective is to calculate the variance of this portfolio, which means I have to calculate the variance of a $R_{ij}$ return and the covariance between $R_{ij}$ and $R_{kl}$. Notice that $i \neq j$ and $k \neq l$, because if it weren't the case, then I would be calculating the return of, for instance, USD/USD.
So the variance of the return of portfolio is (I omit the covariances for simplification and $\omega_{ij}$ is the weight of the asset):
$$Var(R_{p}) = \omega_{12}^2Var(R_{12}) + \omega_{13}^2Var(R_{13}) + \omega_{14}^2Var(R_{14}) + \omega_{23}^2Var(R_{23}) +\omega_{24}^2Var(R_{24}) + \omega_{34}^2Var(R_{34}) + \dots$$
This is where I am facing some difficulties. Usually, $i$ and $j$ are used to represent different assets, so I could denote the covariance between asset $i$ and asset $j$ as $Cov(R_{i}, R_{j})$ and I would have $Var(R_{i})$ and $Var(R_{j})$, which would be the variances of different assets. However, $Var(R_{ij})$ is a single variance. $Var(R_{12})$ and $Var(R_{13})$ represent $Var(USD/GBP)$ and $Var(USD/EUR)$. It makes no sense to write $Var(R_{11})$ because it represents $Var(USD/USD)$, or to write both $Var(R_{12})$ and $Var(R_{21})$ because they are $Var(USD/EUR)$ and $Var(EUR/USD)$, which are the same.
So I have to index the summation operator in a way that $i$ and $j$ respect these restraints. If I simply wrote $\sum_{i}\sum_{j}Var(R_{ij})$, I would be accounting for $Var(R_{11})$ and I would writing both $Var(R_{12})$ and $Var(R_{21})$.
So, my question is: how do I write $i$ and $j$ as a function of $n$ (or $c$) in a way that when I expand the summation operator, I have only $R_{12}$, $R_{13}$, $R_{14}$, $R_{23}$, $R_{24}$ and $R_{34}$. It's not sufficient that $i$ and $j$ are different, because I also cannot account for both $R_{12}$ and $R_{21}$ and so forth. Even though I have six returns and four currencies, $i$ only assume values between $1$ and $2$ and $j$ between $2$ and $4$. Also, I gave an example with only four currencies, but I could have more than thirty.
I am sorry if I rambled too much, I wanted to describe the problem as clearly as possible.
Thanks in advance.
Something like $\displaystyle{\sum_{i<j}}\omega_{i,j}^2\mathrm{Var}\left(R_{i,j}\right)$ would be clear in context.