# Otter's tree growth constant

Christian G. Bower bowerc at usa.net
Tue Apr 18 22:34:23 CEST 2006

One of the standard sources for that type of math is Andrew Odlyzko's book
_Asymptotic Enumeration Methods_ available at:

http://www.dtc.umn.edu/~odlyzko/doc/asymptotic.enum.pdf

His treatment of the tree problem is in Section 10.5, page 103.

My quick glance tells me that it is basically stating and proving the
theorems, but not going through the algorithms in detail in the way that
Harary, Robinson and Schwenk do in "20 step algorithm for determining the
asymptotic number of trees of various species." which I don't believe is
freely available on the web.  I know I have a hard copy somewhere from when I
was helping Steve Finch with some other tree enumeration problems.

I believe Steve had to remove articles from his web page that were used in his
book.  I don't think the Otter article gave all that much information about a
method to calculate the constant to high accuracy.  I do remember that the
2.955765... constant is the reciprocal of the radius of convergence of the
g.f. of A000081 and I think the function's value was 1 at the ROC.

I think the best source would be the H/R/S paper if you can get a hold of it.
Also, you might try contacting David Broadhurst.  (He used to be on seqfan,
but my latest download of the mailing list does not show him.)  Maybe if you
contact Steve, he'll remember enough of it.

One other note: I found a sci.math.research posting by Steve from Nov 28 2001
where he asks a question about an erroneous calculation in H/R/S.  The message
reveals some details about the algorithm.  You can see the message here:

Christian

------ Original Message ------
From: franktaw at netscape.net
To: seqfan at ext.jussieu.fr
Subject: Otter's tree growth constant

> Can someone direct me to a current on-line reference for how to compute
> this constant (A051491)?  The 1800 digit value on Plouffe's page is
> there, but the link for Finch no long seems to point to anything
> relevant.
>