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Kid has a math homework I can't figure out. What are the next 3 numbers in this sequence?
2, 12, 36, 80
[Teacher rarely makes typos, this is not meant to be a trick question, etc. This is late middle-school, so leave your fancy trig-and-beyond at home.]
[Edit: Yes, I did look it up in OEIS. But I was implicitly curious about how people found the solution.]
@shriramk I hate these problems because there's always some implied or assumed formula. The unsatisfying (but IMO correct) answer is: As presented, there is not enough information to solve this problem.
One solution they may be looking for is:
2, 12, 36, 80, 150, 240, 356, ...
[Edit: To quote Bob the Flower, "This is wrong!" See below.]
@inthehands @shriramk Eventually I got my differences correct. I repeated that until I ran out of known differences so I just assumed the lowest band of differences was constant (value 6). Backworked the other terms in the triangle (trapezoid, really) until I got the next three elements. I still have my discrete math textbook from ~35 years ago and it probably explains how to convert that to the solution listed in OEIS
@inthehands @shriramk Apologies for the (lack) of formatting:
2 12 36 80 150 252 392
10 24 44 70 102 140
14 20 26 32 38
6 6 6 6
and so on.