Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 7 Marks

Year: May 2014

The characteristic equation of the recurrence relation is $r^3+3r^2+3r+1=0$ Its roots are r=-1. Hence the sequence {$a_n$} is a solution to the recurrence relation if and only if

$a_n=α_1 (-1)^n+-α_2 (n)(-1)^n+α_3 (n \times n)(-1)^n=α_1+α_1n+α_3(n \times n)$

For some constant $α_1$ and $α_2$.

From the initial condition, it follows that

$a_0=5=α_1 …