MathCastle
Counting & ProbabilityChallengeRecursion, Catalan Numbers & Generating Functions

Recursion, Catalan Numbers & Generating Functions · Challenge problem

How many sequences (a1,a2,…,a10)(a_1,a_2,\dots,a_{10}) with every ai∈{1,2,3,4}a_i\in\{1,2,3,4\} satisfy ∣ai+1−ai∣≤1|a_{i+1}-a_i|\le1 for i=1,2,…,9i=1,2,\dots,9?