
difference equations
needed help for these three questions if possible?
1) let Yn stand for the number of strings of length n in letters abcdefghijklm such that no two are consectutive entries lie in set{ a,b,l,m}
(i) find y1 y2 and a diffdernece eqn for Yn+2 in terms os Yn and Yn+1
and solve this equation and find a formula for yn.
(b)let Yn stand for the number of strings of length n in digits 0,1,2....,9 in which 3 occurs an odd number of times. find a first order differnece equation for yn, and hence find a formula for yn in terms of n.
(c)let Rn be the greatest number of regions that the plane is divided into by n circles. find the values of r1,r2,r3,r4.
find a difference equation for rn, and solveit, find an explicit formula for Rn.
Many thanks to anybody that could help me..