the sequence A006743

[Thomas Baruchel]

On Lun, oct 17, 2005 at 10:29:49 -0700, Max wrote:
> What method do you use to discover such recurrences?

Hi,

I know perfectly that you wrote to Simon Plouffe and asked about
special recurrences involving the index n, but if you are also
interested by simple linear recurrence, I have worked much on them
last times. Have you ever noticed that the coefficients of the
linear recurrence are given by the coefficients in the denominator
of the Padé approximant for the McLaurin serie:
  a(0) + a(1) x + a(2) x^2 + a(3) x^3 + ...
If you have 10 terms, just take the McLaurin serie up to degree 9.
Then compute the simplest Padé approximant for that degree of precision,
and you have the recurrence formula ! (If there are several Padé
approximant, take the one with the simplest denominator).
With a computer algebra system, it is ONE command.

Hope you are interested,

regards,

-- 
Thomas Baruchel
  Home Page: http://baruchel.free.fr/~thomas/