[seqfan] A072030 and computing A113881.

[Peter Luschny]

I would like to understand better the relation between

A072030 (number of steps in Nicomachus' algorithm) (see [1]) and
A113881 (smallest number of squares needed to tile an m x n rectangle).

What I mean can be easily seen by comparing the tables
http://oeis.org/A072030/table and http://oeis.org/A113881/table .

Is there a simple (not necessarily efficient) algorithm to compute A113881?
In particular I would like to know if the simple recurrence given in
A072030 can be used to advantage in computing A113881?

Peter

[1] http://archive.org/details/NicomachusIntroToArithmetic (pages 206 and
207)
[2]
http://pageperso.lif.univ-mrs.fr/~alain.colmerauer/ArchivesPublications/Gambini/carres.pdf
[3] http://www.sciencedirect.com/science/article/pii/S0097316596901041#(open
access)
[4] http://squaring.net/sq/tws.html
[5] http://projecteuclid.org/euclid.dmj/1077492259 (access denied)