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This sequence is wrong because of a bug in Mr . Parkin's code, and amazingly I can pinpoint exactly what the bug is! (I can reproduce his results.)
Firstly the description of the problem and its solution in Mr . Parkin's letter is very clear - - he doesn't leave a lot of room for misinterpretation (this is hugely to his credit). He also includes a very clear description of his algorithm, so I decided I would just code it up. I obtained _Giovanni Resta_'s results as given in A257952 - - there is nothing wrong with Mr Parkin's algorithm.
A detailed break-down breakdown of Parkin's results is also provided in the letter. All the results match with the exception of the final line. (This would be highly improbable if there was a completely different interpretation.) In any case, one sentence stood out as a possible red flag: "Further, there are potential mirror image paths in both cases when starting on the centre lines and these are prevented by requiring a turn in one direction on the path prior to allowing a turn in the other direction" (bottom of page 6). The discrepancy in results does indeed relate to the centre center line and if I modify my code to lose the flag on recursion, then I get Mr . Parkin's results (so turn in one direction is only prohibited for one step). (End)
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Comment from Andrew Howroyd, Apr 18 2016 : (Start):
This sequence is wrong because of a bug in Mr Parkin's code, and amazingly I can pinpoint exactly what the bug is! ( I can reproduce his results).)
A detailed break-down of Parkin's results is also provided in the letter. All the results match with the exception of the final line. (this This would be highly improbable if there was a completely different interpretation). ) In any case, one sentence stood out as a possible red flag: "Further, there are potential mirror image paths in both cases when starting on the centre lines and these are prevented by requiring a turn in one direction on the path prior to allowing a turn in the other direction" (bottom of page 6). The discrepancy in results does indeed relate to the centre line and if I modify my code to lose the flag on recursion, then I get Mr Parkin's results (so turn in one direction is only prohibited for one step). (End)
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