Question

Find a recurrence relation for the number of strictly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. that is, sequences a1, a2,...,ak, where a1 = 1, ak = n, and aj < aj+1 for j = 1, 2,...,k − 1.
b.what are the initial conditions?

c.how many sequences of the type described in (a) are there when n is an integer with n ≥ 2?

Answer 1

Answer:

Step-by-step explanation:

(1)

$a_i = a_{i-1} + 1$

(2)

The initial condition is $a_1 = 1$

(3)

Infinitely many.