Observations on Motzkin numbers

[Meeussen Wouter (bkarnd)]

ID Number: A064189
Sequence:  1,1,1,2,2,1,4,5,3,1,9,12,9,4,1,21,30,25,14,5,1,51,76,69,44,
Name:      Motzkin triangle, T, by rows, read in reverse order: 
See also:  Triangle in A026300 (the main entry for this sequence) with rows
read in reverse order.


looks ok to me. Following the links gets me there.

Wouter Meeussen



-----Original Message-----
From: David Wilson [mailto:davidwwilson at attbi.com]
Sent: vrijdag 31 januari 2003 14:00
To: Sequence Fanatics
Subject: Observations on Motzkin numbers


A001006 is the Motzkin numbers, while A064189 is the Motzkin triangle.
We have A001006(n) = A064189(n, 0).  The two sequences should reference
one another.

Also, A001006 gives the number of ways of drawing any number of
nonintersecting chords between n points on a circle, while A054726 gives
the number of ways of drawing noncrossing chords between n points on a
circle.  The difference is that nonintersection chords have no point in
common, while noncrossing chords may share an endpoint.  I think A001006
and A064189 should reference one another.  Also, I was wondering if there
would be formulae for A001006 analogous to the many formulae for A001006,
especially the Motzkin triangle.


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