[seqfan] Re: 8/5 Sequence
Maximilian Hasler
maximilian.hasler at gmail.com
Wed Sep 30 15:07:11 CEST 2009
> (Is A128587 a signed version of A001595?
> http://www.research.att.com/~njas/sequences/?q=id%3AA001595|id%3AA128587
> )
Up to offset and initial terms, yes:
This follows e.g. from
%F A128587 G.f.: -x*(1+3*x+3*x^2)/((1+x)*(x^2-x-1)).
and
%F A001595 G.f.: (1+x-x^2)/(1-2*x+x^3).
If you take the g.f. of A128587, subtract x+x^2 to eliminate the two
initial terms, divide by x^3 to start at offset 0, then you get the
g.f. of A001595 with x replaced by -x.
Thus,
A128587(n+3) = (-1)^n * A001595(n) for all n>=0.
Maximilian
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