Triangular number recurrence ($T_n-T_{n-1}=n$)

For a positive integer $n$, adding the row of length $n$ to the previous arrangement gives $T_n=T_{n-1}+n$. Thus the first differences of the triangular numbers are $1,2,3,\dots$. The triangular number recurrence provides incremental computation: after $T_6=21$, adding seven gives $T_7=28$.