The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each subsequent row contains one more element than the previous one. This is illustrated above for T_1=1, T_2=3, .... The triangular numbers are therefore 1, 1+2, 1+2+3, 1+2+3+4, ..., so for n=1, 2, ..., the first few are 1, 3, 6, 10, 15, 21, ... (OEIS A000217). More formally, a triangular number is a number obtained by adding...
