# Witt transform examples in the OEIS

franktaw at netscape.net franktaw at netscape.net
Thu Jul 31 01:48:44 CEST 2008

```The diagonals k = n+1 and k=n-1 sure look like the Catalan numbers.
The diagonal k = n looks like
http://www.research.att.com/~njas/sequences/A022553, the
number of Lyndon words, which also seems reasonable.  Are these
correct?  (Some of the references in A022553 might also be
relevant.)

IMO, yes, the matrix should definitely be submitted.

-----Original Message-----
From: Jonathan Post <jvospost3 at gmail.com>

So, Richard Mathar, is it worth your submitting the matrix, read by
antidiagonals
A[k,n] = n-th value of k-th Witt transform of A000012
which begins:

.......|..n=0.|.n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|.n=7.|.n=8.|
k=1.|....1...|...1...|....1..|....1..|...1..|...1...|...1...|.....1..|...
1..|.
k=2.|....0...|...1...|....1..|....2..|...2..|...3...|...3...|....4...|...
4..|.
k=3.|....0...|...1...|....2..|....3..|...5..|...7...|...9...|...12...|.15
..|.
k=4.|....0...|...1...|....2...|...5..|...8..|..14..|..20...|..30...|..40.
|.
k=5.|....0...|...1...|....3...|...7..|.14..|..25..|..42...|..66...|..99.|
.
k=6.|....0...|...1...|....3...|...9..|.20..|..42..|..75...|.132..|.212.|.

k=7.|....0...|...1...|....4...|.12..|.30...|.66..|.132..|..245.|.429.|.

and so forth?

Anything to say about the columns?

And what is the main diagonal?

...

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