Investigating Special Binary Sequences with Some Computer Help

In this note, we study exclusively n-length binary sequences where at least one 1 is adjacent to (or touching) another 1. For brevity, we refer to them as “binary sequences with some touching 1’s.” They are not to be confused with n-length binary sequences where every 1 is adjacent to at least one other 1 [1]. We let C n denote the collection with unrestricted content, and we let D n denote the subset of C n with even content. (Content is defined as the number of 1’s in a binary sequence.)