Problem
COM-B1-M11-P011 Strings
#11
★★☆☆☆ Level 2 of 5
How many binary strings of length \(7\) contain no two adjacent ones?
Last symbol \(0\) or final block \(01\).
Let \(a_n\) be the number of such strings. Then \(a_0=1\), \(a_1=2\), \(a_n=a_{n-1}+a_{n-2}\). We get \(a_7=34\).
Recurrence in mixed practice.