Nomenclature for number of self-references in a recursive sequence

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I am looking for a word that denotes the number of self-references in a recursive sequenece. For example, the Fibonacci sequence is defined by the recurrence relation $F_n = F_{n-1} + F_{n-2}$, and so it could be said that the word I am looking for of the Fibonacci sequence is 2.

I have scoured the Wikipedia articles on sequences and recursion, without coming across a satisfactory answer. Intuitively, I would go for something along the lines of recursion depth, but this already has a different meaning in computer science.

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The term you're looking for is order.

For instance, the Fibonacci sequence is a homogeneous linear recurrence of order $2$.