By Aaron Robertson, Herbert Wilf, and Doron Zeilberger
Written: April 17, 1999
(Appeared in Electronic J. Combinatorics v. 6 (1999), R38).
This article started out as a heavy-duty symbol-crunching
sequel of a previous human-insight-heavy article by
Aaron. Then Herb came along, and using beautiful human insight,
found an EXPLICT and AMAZING expression, in terms of
a Rogers-Ramanujan-like continued fraction, for the
generating function, which, as a bonus, implied a super-fast
algorithm for computing what we call in the paper
AR(r) and Aaron(r). Just for comparison, with the
original, slow, algorithm (that is kept in the
Maple version, downloadable below, for old-time's sake, and
for comparison and check, as AaronSlow), it took all night
to find Aaron(4), and now it takes a few seconds. Just
type `Aaron(4);' .
Doron Zeilberger's List of Papers
.pdf
.ps
.tex