# Counting graceful paths

How can one count the number of graceful labelings of a path graph?

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in the fifth talk in this list it is conjectured order $\log(n)\log(n−1)\dots \log(2)$ facstaff.unca.edu/pbahls/GGGstuff/2008/… –  Pietro Majer May 31 '11 at 8:44
Nice, thanks. I guess I had thought there would be a closed formula! –  Dr Shello Jun 2 '11 at 0:43

## 1 Answer

An efficient algorithm is described in a paper by Michael Adamaszek which is powerful enough to count the number of graceful labelings of paths up to length 40. It concludes: "It also remains an open question to find an exponential upper bound on [the number of graceful labelings of paths of length n]"

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by the same author: oeis.org/A006967 –  Pietro Majer May 31 '11 at 12:33