A120011 and A127275

Max Alekseyev maxale at gmail.com
Tue Jun 17 18:36:11 CEST 2008

Actually, the generating function listed in A120011 is not reduced
(the numerator and denomerator share the common factor 1-4x):

A(x) = x*(3 - 12*x - 2*(1-4*x)*C(x) ) / (1-4*x)^2 = (3*x - 2*x*C(x)) / (1-4*x)

Plugging in C(x) = (1-sqrt(1-4*x))/(2*x) results in:

A(x) = (3*x - 1 + sqrt(1-4*x)) / (1-4*x) = -1 + (sqrt(1-4*x) - x)/(1-4*x)

which proves the specified relationship between A120011 and A127275.

I think A120011 can be simply removed in favor of the following
comment to A127275:

%C A127275 The 2-nd self-compose of g.f. G(x) of A120009 is G(G(x)) =
(sqrt(1-4x)-x)/(1-4x) - 1.


On Sat, Jun 14, 2008 at 12:18 PM, Richard Mathar
<mathar at strw.leidenuniv.nl> wrote:
> Given that A127275 and A120011 are almost the same, and that the
> generating functions are described in some detail, it seems to be manageable
> to simplify A120011 based on this, and to show that they only differ
> by the additional leading number in A127275.
> Richard


Thanks very much for editing all those sequences!

I appreciate your help (and Maximilian's)

New version of the OEIS with all these
entries in a few minutes

(except I have not finished reading emails from the
past week, so there may be more in the pipeline)

By the way, this person submitted a lot more entries,
of the same type, and still not using the web page.
I rejected them, and told him I could not accept

(Since they were all very uninteresting sequences, 
- just as the ones you edited turned out  in the end
not to be very interesting -
I figured there would be no loss if he did not do so)

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