Let $k > 0$ be an integer.
Define $A_n$ as follows:
$$ A_n = \begin{cases} n & \text{if } n < k, \\ \sum_{i=0}^{k-1} i & \text{if } n = k \\ \sum_{i=1}^k A_{n-i} & \text{if } n > k. \end{cases} $$
This looks much like Fibonacci, except it's linear up until the k-th term (so the G formula does not work). I am 99% sure there is a closed formula for this one, but can't seem to figure it out at the moment.
Any pointers will be appreciated!
