We exhibit a recurrence relation for $r_k (n)$, that is, for the number of representations of a positive integer as a sum of squares, so it is possible to determine $r_k (n)$ if we know $r_k (m) , m=0, 1, 2,\ldots, n-1$.
t: We exhibit polynomial expressions for the arithmetic functions and , the number of
representations of n as a sum of k squares and k triangular numbers, respectively, and also for the color partitions
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