Bug introduced in 9.0.1 and fixed in 10.0.0


RSolve[{a[n + 1] == 2 a[n] + n (1 + 2^n), a[1] == 1}, a[n], n]

Mathematica 8 can solve this quickly, but Mathematica 9, even after being allowed to run for a long time, cannot give a result.

  • 5
    $\begingroup$ Strange, but this works : RSolve[{a[n + 1] == 2 a[n] + b[n], a[1] == 1}, a[n], n] /. b[m_] -> m (1 + 2^m). $\endgroup$ Commented May 1, 2014 at 5:07
  • 2
    $\begingroup$ I can confirm this behavior and think it is a bug. I have sent WRI tech support a report of this problem. I will post their answer when I receive it. $\endgroup$
    – m_goldberg
    Commented May 1, 2014 at 6:32
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    $\begingroup$ @m_goldberg C'mon! It's clearly a feature! $\endgroup$ Commented May 1, 2014 at 7:27
  • $\begingroup$ Sometimes internal functionality gets improved by making it more flexible, but in the course of doing so a good hard-coded algorithm that solves a specific problem gets broken. $\endgroup$ Commented Mar 12, 2016 at 16:35

1 Answer 1


I submitted a report about this problem to WRI tech support. I have received their reply and quote it part below.

Thank you for bringing this RSolve issue to our attention.

I can reproduce the situation you found on both Mathematica 9 and Mathematica prerelease and have filed a report on it.

I think it is safe to tag this question with .


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