Ludwig Seidel's remarkable algorithm

[Peter Luschny]

Hello to all!

Ludwig Seidel published in 1877 a remarkable algorithm,
simple and efficient, to compute the coefficients of the
secant and the tangent numbers as well as the Bernoulli numbers.

Seidel remarked that the flow of the computation
has a boustrophedon pattern. This means you 'plow' across
an integer triangle from right to left, then turn around and
'plow' from left to right, and so on.

This month I wrote in my blog at OEIS about Seidel's algorithm
and a way to generalize it -- to a boolophedon algorithm, as
I called it -- to compute the generalized Euler Numbers A181985
and the André Numbers A181937.

http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform

Hope you enjoy it.

Peter        

Plowing-by-Hand in Osiris's House-Two Lands (of Egypt).
Public domain worldwide.

[Neil Sloane]

Peter, May I draw your attention to the paper that Jessica Millar,
Neal Young and I wrote
on this subject:

211. A New Operation on Sequences: The Boustrophedon Transform
[Abstract, postscript, pdf, arXiv:math.CO/0205218], J. Millar, N. J.
A. Sloane and N. E. Young, J. Combinatorial Theory, Series A, 76
(1996), pp. 44-54.

(that is from my home page (http://NeilSloane.com), item 211 under
Publications)

Neil

>  640px-Maler_der_Grabkammer_des_Sennudem_001.jpg
> 154KViewDownload

[Peter Luschny]

> Peter, May I draw your attention to the paper that Jessica Millar,
> Neal Young and I wrote on this subject:

Dear Neil, thank you for your interest.

In the blog I only focus on the algorithm and its implementation, not
on the mathematical representation. I also wanted to draw some
attention to Seidel's original paper, as it seems that it is still
little known (and it is not yet digitized, as far as I know).

I have read your paper some times ago and I will reread it and
add a reference to my blog.

Peter