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.

(In reply to an observation by Dej Mar)

Interesting, and valued.

I had derived that (3nē + 9n +8)/2 was the sum of 3 consecutive triangular numbers.  My issue was to determine a unit incremental value that would create that 'n'.

The formula offered, x = SQRT(3n² + 9n + 33/4) - (1/2), equates to the Sloane sequence A082840 only when 'x' is an integer for unit increments of 'n'.

Edited on November 30, 2009, 7:18 pm

Posted by brianjn on 2009-11-30 08:13:20