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 possible^{1}) 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(3n^{2} + 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 20091130 08:13:20 