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Given a sequence $a_1, a_2, \ldots$ the first difference is $b_1, b_2, \ldots$ where $b_i = a_i - a_{i-1}$. However, I have not been able to find what the following is called:

$$c_i = a_i - a_{i-k}$$

for some $k$. What would this "skipping" difference be called? For example, the "2-skipping" first difference of the square numbers would be: $9-1, 16-4, 25-9, $ etc.

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  • $\begingroup$ You can write it as $(a_i - a_{i-1}) + (a_{i-1} - a_{i-2}) + \ldots + (a_{i - k+1} - a_{i-k})$. Thus, the k-skipping can be rewritten as a sum of terms of the first difference. $\endgroup$ – астон вілла олоф мэллбэрг Mar 27 '17 at 3:59
  • $\begingroup$ By the above comment, I mean to say that whatever you call it, it is enough to analyse the terms of the first difference. $\endgroup$ – астон вілла олоф мэллбэрг Mar 27 '17 at 4:10

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