Can You Solve This Combinatorics Problem Involving Arrangements of X and Y?

[physicsmath94]

given a chain of n terms with each term either being x or y, how many arrangements are there such that you don't have any two terms being x next to each other.

for example if n= 5

(x,y,y,y,x) ; (x,y,x,y,x) are acceptable while (y,x,x,y,x) is not acceptable.

Generalize this result for all values of n.

 

[tiny-tim]

welcome to pf!

hi physicsmath94! welcome to pf!

Show us what you've tried, and where you're stuck, and then we'll know how to help!