http://www.research.att.com/~njas/sequences/A099856 Expansion of (1+3x)/(1-3x). matches an ongoing computation of 1/20 the number of (n+1)X2 arrays of integers in 1..5 with no element or any of its neighbors having the same value which I guess shows the virtue of sometimes dividing by the first term. rhhardin at mindspring.com rhhardin at att.net (either)