No Two Alike in a Row
A composition of 10 is an ordered sum of positive integers equal to 10 (so 1 + 2 and 2 + 1 are different compositions of 3). How many compositions of 10 have no two adjacent parts equal? For example 3 + 1 + 2 + 4 qualifies, but 3 + 3 + 4 does not. The one-part composition 10 qualifies. Give an integer.
Related problems & prerequisites
Worth solving first
- Dominoes and Big Squares 4.0/10
- Tiling with Dominoes 3.9/10
- No Consecutive Elements 3.5/10
Source: Such compositions were studied by L. Carlitz (1976). Statement written for AxiomIQ.