A small factors sequence

[Creighton Dement]

A link to first 200 terms of the sequence factored:
http://www.crowdog.de/smfactors.html

Sincerely, 
Creighton 


- It's a shame when the girl of your dreams would still rather be with
someone else when you're actually in a dream.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

> Date: Sun,  4 Dec 2005 21:08:50 +0100
> Subject: Re: A small factors sequence
> From: Gerald McGarvey <Gerald.McGarvey at comcast.net>
> To: "Creighton Dement" <crowdog at crowdog.de>, seqfan at ext.jussieu.fr

> An observation about the sequence a(n):
> If a difference 'triangle' is formed by repeatedly taking the
> differences b(n+6) = a(n+6) - a(n)
> c(n+12) = b(n+12) - b(n+6) etc.
> then the 7th iteration of these differences are
> 279936, -279936, -559872, -279936, 279936, 559872, 279936, -279936 the
> 8th differences are zero, and the 6th iterations also have small
> factors, but not all the terms in this 'triangle' have small factors.
> I don't know if this
> can help at all to explain the small factors, and I'm not following
> how the sequence comes from the formula (I don't have Maple).
> A curiosity: no term before a(43) is divisible by 7, but a(43) through
> a(49) are all divisible by 7.
> 
> Sincerely,
> Gerald
> 
> At 07:57 PM 12/3/2005, Creighton Dement wrote:
> 
> > Dear Seqfans,
> > 
> > I came across a sequence given in Maple by
> >
seriestolist(series((1-16*x+56*x^3-140*x^4+28*x^6-16*x^7+28*x^2+56*x^5+x^8)/(x^2-x+1)^8,
> > x=0,50));
> > 
> > 1, -8, -72, -120, 330, 1584, 1716, -3432, -12870, -11440, 19448,
> > 63648, 50388, -77520, -232560, -170544, 245157, 692208, 480700,
> > -657800, -1776060, -1184040, 1560780, 4071600, 2629575, -3365856,
> > -8544096, -5379616, 6724520, 16695360, 10295472, -12620256,
> > -30761874, -18643560, 22481940, 53956656, 32224114, -38320568,
> > -90759240, -53524680, 62891499, 147258144, 85900584, -99884400,
> > -231550200, -133784560, 154143080, 354201120, 202927725, -231917400
> > 
> > By chance, I noticed that each term of the above sequence (in the
> > range given) has small factors.  Pardon me for asking a vague
> > question, but does the above sequence illustrate anything of
> > interest in particular? 
> > p.s. I have visitors at the moment and, unfortunately, won't be able
> > to look at the above again in detail until next week (though I am
> > quite fortunate to have visitors!)
> > 
> > Sincerely,
> > Creighton
> > 
> > -It's a shame when the girl of your dreams would still rather be
> > with someone else when you're actually in a dream.
> > 
> 
>