Adieu (fwd)
Richard Guy
rkg at cpsc.ucalgary.ca
Thu Jan 11 17:21:20 CET 2007
I haven't received a copy of this, so perhaps
my request to be cut off was implemented even
before I made it! I send again, also using
the old (?) address. R.
---------- Forwarded message ----------
Date: Wed, 10 Jan 2007 19:59:49 -0700 (MST)
From: Richard Guy <rkg at cpsc.ucalgary.ca>
To: seqfans at seqfan.net
Subject: Adieu
Sequence fans,
Swan song.
1. Helena Verrill, in a talk at
New Orleans on Series for 1/pi
mentioned ``Almkvist - Zudilin
numbers''
1 -3 9 -3 -279 2997 -19431
which I don't find in OEIS, but
then, as my Mother said, I'm not
a good looker.
2. In a paper written with Alex Fink & Mark Krusemeyer there
is the following table. These sequences have a good deal in
common, but what is common is not always recorded at each
sequence. I will elaborate on this in a message to Neil's
Dream Team before much more water has flowed under the
bridge.
\begin{center}
\begin{tabular}{cc|cc|cc|cc|cc}
$r$ & OEIS \# & $r$ & OEIS \# & $r$ & OEIS \# & $r$ & OEIS \# & $r$ & OEIS \#
\\
--14 & \ldots & --8 & A070998 & --2 & A001519 & 4 & A002878 & 10 & A057081 \\
--13 & A001570 & --7 & A070997 & --1 & A000012 & 5 & A001834 & 11 & A054320 \\
--12 & A085260 & --6 & A049685 & 0 & A011655 & 6 & A030221 & 12 & A097783 \\
--11 & A077417 & --5 & A001653 & 1 & \ldots & 7 & A002315 & 13 & A077416 \\
--10 & A078922 & --4 & A004253 & 2 & A057079 & 8 & A033890 & 14 & \ldots \\
--9 & A072256 & --3 & A001835 & 3 & A005408 & 9 & A057080 & 15 & A028230
\end{tabular}
\end{center}
3. Also arising from this paper is an iterative process,
which may be familiar to most seqfans, but which I don't
seem to be able to tie up with anything in OEIS. Here's
a not very good example, because the degrees of the
polynomials go up too fast. Start with an array, say
the Omar Khayyam triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
.........................
and then write the diagonals as polynomials, whose
coefficients, after normalization by (-1)^r * r!
form the array
1
0 1
0 1 1
0 2 3 1
0 6 11 6 1
0 24 50 35 10 1
0 120 274 225 85 15 1
.............................
which, in this case, I believe to be Stirling
numbers of the first kind. The diagonals are
A000012, A000217, A000914 (or A115057 -- is
this different?), A001303, ... . Repeat the
process, yielding
1
0 1 1
0 10 21 14 3
0 1 11 47 97 96 36
..............................
(are these in OEIS ? Schroeder numbers ???
this done by hand, and probably containing
errors) and repeat the process ad lib ...
The array formed by the sequences listed
under 2. above form a similar, but in some
ways more interesting example, and presumably
many of the arrays in OEIS will also yield
sequences of arrays which will be of interest.
4. I reluctantly request that I be removed
from the seqfan list since the messages have
reached a volume, and have often a content,
matched only by the spam that I receive. I
will send to Neil, or to his Dream Team, if
I have any serious comments or queries about
OEIS, a beautiful project which I have seen
grow since I first met Neil over 40 years ago.
Best wishes to all serious contributors --
they know who they are. R.
More information about the SeqFan
mailing list