In previous work ( Part I, Part II, Part III), **running equalities** are written in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. Each digits is used once with basic operations, along with factorial, square-root and Fibonacci sequence values. These types of equalities, we called as **running expressions**. This work bring running expressions with double and triple equality signs using **Triangular sequence numbers **along with basic operations. The work is up to 3 digits in increasing and decreasing orders. Four digits onwards the results shall be studied elsewhere. See below examples and link for download the work:

I.J. TANEJA, Running Expressions with Triangular Numbers – I, **Zenodo**, Open Acess, Dec 21, 2018, pp.1-142, https://zenodo.org/record/2483327.