  The enumeration of the regions formed when circle is divided by secants drawn
from points on the circle is one of the examples where the inductive reasoning
fails as was pointed out by Leo Moser in the Mathematical Miscellany in 1949.
The formula that gives the right number of regions can be deduced by
combinatorics reasoning using the Euler's planar graph formula, etc. My
contribution in the present work is to reformulate and solve such problem in
terms of a fourth order difference equation and to obtain the formula proposed
by Leo Moser.
