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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 cowan@xxxxxxxx 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)