# An recurrence equation that can be solved in version 7 but not in version 8

A friend of mine showed me this code sample:

RSolve[{a[n] == a[n - 5] + 1, Sequence @@ Table[a[i] == 1, {i, 5}]}, a[n], n] // Timing


It's solved by version 7 in about 40s, while in version 8 it keeps running for more than 10 minutes… is it a bug?

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It is interesting that the same problem, with $5$ changed to $4$, is solved in less than $0.1$ seconds with MMA 8, and with $5$ changed to $7$, the solution also takes less than $0.1$ seconds (although it's trivially expressed in terms of DifferenceRoot, which is just another way of giving up). With $5$ changed to $6$, a useful solution is obtained in $6$ seconds. –  whuber Dec 21 '12 at 17:58