Talk:Motzkin number
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Extraneous "1"?
[edit]It appears that the list obtained from OEIS contains an extra "1" at the beginning. I removed it, then readded it since it is required given the mathematical definition on Wolfram Mathworld, but I welcome a correction with some explanation if this is erroneous. The second 1 does not fit the path definition or chord drawing examples given, but mathematically n=0 does produce a 1 result. The OEIS page conflicts with the Wolfram Mathworld list, which appears to be logically consistent, but ignores n=0. LUxlii (talk) 20:46, 23 May 2013 (UTC)
Chords on a Circle
[edit]The description of Motzkin numbers as describing the drawing of chords between points on a circle seems incomplete and possibly misleading. The Wolfram Mathworld page indicates that "The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the number of paths from (0, 0) to (n, 0) which never dip below y=0 and are made up only of the steps (1, 0), (1, 1), and (1, -1)..." I can visualize the sequence using the description on Wolfram Mathworld, but my visualization fails with the chord drawing example for n=3 (3 ways?). Does this need more discussion (ideally from someone far more knowledgeable than I)? LUxlii (talk) 21:03, 23 May 2013 (UTC)