For what it's worth mathematics is more than flexible enough to handle both 0 and 1 based indexing. Using 1 based just looks neater since you can count x_1, ..., x_n rather than x_0, ..., x_{n-1}. Sometimes both are used at the same time e.g. if you add an extra coefficient at the start rather than at the end, this happens particularly when dealing with wedge products where the parity of the new index matters.

Also it's usually a bad sign if you need to worry too much about what index you used, you might be better of using index sets with whatever structure you need (and only the structure you need). In program languages that support it generous application of ranges and generators tends to get rid of most complications.