A quotient-difference table is a triangular Array of numbers constructed by drawing a sequence of numbers in a horizontal
row and placing a 1 above each. An additional ``1'' is then placed at the beginning and end of the row of 1s, and the value of
rows underneath the original row is then determined by looking at groups of adjacent numbers
0s in quotient-difference tables form square ``windows'' which are bordered by Geometric Progressions. Quotient-difference tables eventually yield a row of 0s Iff the starting sequence is defined by a linear Recurrence Relation. For example, continuing the above example generated by the Fibonacci Numbers
See also Difference Table, Finite Difference
Conway, J. H. and Guy, R. K. In The Book of Numbers. New York: Springer-Verlag, pp. 85-89, 1996.