Oops, sent too soon.  Calkin and Wilf's original paper is online at
<http://www.math.upenn.edu/~wilf/website/recounting.pdf>.  And I meant
to mention that I thought up the naive diagonal approach described in the
first paragraph of Gibbons, Lester, and Bird myself in 1975 (I was in high
school) in order to implement sparse matrices on top of sparse vectors.
The redundancy there was actually desirable, since you don't want A[1,2]
to be the same as A[2,4].

--
John Cowan          http://www.ccil.org/~cowan        xxxxxx@ccil.org
I Hope, Sir, that we are not mutually Un-friended by this Difference
which hath happened betwixt us.
     --Thomas Fuller, Appeal of Injured Innocence (1659)