A, B, C and D are triangular numbers.

A, B and C are always consecutive while D is their sum.

Determine (and explain as best as possible¹) how such sets of values are distributed across the number system.

^1. This can be explained in terms of a single variable expression.

The ordinal number x of a triangular number T_x which is the sum of three consecutive triangular numbers can be found where
x = SQRT(3n² + 9n + 33/4) - (1/2)
such that x is an integer and n is the ordinal number T_n of the first of the three consecutive triangular numbers.

Posted by Dej Mar on 2009-11-30 04:40:05