[seqfan] Re: LRS formulas for n>=...?
rhhardin at att.net
rhhardin at att.net
Sun Aug 2 15:13:23 CEST 2009
[Richard Mathar]
> The interest is in figuring out which other sequences have
> the same combinatorial structure. To make such connection, one needs to gather
> them at some common market place like
> http://research.att.com/~njas/sequences/Sindx_Rea.html#recLCC
> (for which I have some slightly updated version). The idea is that a look-up
> with the (4,-5,2,1,-2,1) signature of the coefficients coeff(i) in front of
> the a(n)=sum_i coeff(i)*a(n-i) leads to other sequences of the same family.
It makes more sense to have that automated, then, doesn't it? The coefs can
be thought of as implicit in the given series, if they're there, at least for
empirically generated ones like mine that just turn up or don't; and some
series crawler will put them in the right index.
If it's automated anyway, adding them manually is just an opportunity for error
and perhaps better left out.
Does the cited page require the entire series obey the formula from the first term?
(I'm getting what must be a boundary condition effect for a few terms, before the
formulas kick in.)
Indeed for a couple they're twice the Fibonacci numbers after several terms, and
the any information is in how they wander around before that starts. (I have no
idea, from how they're computed, how the Fibonacci numbers eventually get there.)
--
rhhardin at mindspring.com
rhhardin at att.net (either)
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