How many r-digit ternary sequences are there in which...

How many r-digit ternary sequences are there in which A) No digit occurs exactly twice? B) 0 and 1 each appear a positive even number of times?

Find an exponential generating function for the number of distributions...

Find an exponential generating function for the number of distributions of r distinct objects into n different boxes with exactly m nonempty boxes.

Recurrence Relation

1) Find and solve a recurrence relation for the number of n-digit ternary sequences with no consecutive digits being equal. 2) Find and solve a recurrence relation for the number of infinite regions formed by n infinite lines drawn in the plane so that each pair of lines intersects at a different point. 3) Find and solve a recurrence relation for the number of different regions formed when n mutually intersecting planes are drawn in three-dimensional space such that no four planes intersect at a common point and no two planes have parallel intersection lines in a third plane. (Hint: reduce to a two-dimensional problem.) 4) Suppose a savings account earns 5 percent a year. Initially ... click for more

Recurrence relation, functional equation...

(See attached file for full problem description with proper symbols and equations) --- 1. Find a functional equation and solve it for sequence of generating functions whose coefficients satisfy (assume and =1): 1. 2. Find a recurrence relation and associated generating function for the number of n-digit ternary sequence that have the pattern "012" occurring for the first time at end of the sequence. 3. Find and solve simultaneous recurrence relation for determining the number of n-digit ternary sequences whose sum of digits is a multiple of 3 ---

Parameters of an octagon

A regular octagon is inscribed in a circle of radius 15.8 cm. Find the parmeters of the octagon.