Triangular numbers are used to unravel a new sequence of natural numbers here-to-fore not appearing on the Encyclopedia of Integer Sequences website. Insight is provided on the construction of the sequence using "buildings" as a viewable model of the sequence entries. A step-by-step analysis of the sequence pattern reveals a method for generating the function. Graphing calculator programs are provided for generating the sequence both recursively and explicitly for different initial "building" sizes. Finally, an explicit formula for the sequence that makes use of the "ceiling" function generalizes the results.