Another variant of my previous question, this one might be easier (or harder).
What is the next number in the sequence $1, 2,6, 16, ...$?
To clarify: the 'hints' are really clues. They are hidden, because any of the two alone could be enough to solve the puzzle. So, anyone who is interested, can look up only one hint, or both.
First hint:
Second hint:
Answer
On the basis of the second hint the answer is evidently
42
unless I have miscalculated. The idea is that you
proceed clockwise and inward to fill the triangle, starting with a 1 at top left and always filling each cell with the sum of the adjacent numbers you have so far. The black cell is the last one to be filled.
I think (but haven't checked) that the idea of the first hint is that
you start with a 1 and form triangles by a clockwise outward spiral, and each time you form a new triangle larger than its predecessor you record the number in its final cell.
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