1. 2 neighbors
2. 8 neighbors
3. 26 neighbors
4. 80 neighbors

That's for all neighbors. As for neighbors near the origin ... that's a completely different set of numbers. And, in 3-D, it's not (2**N - 1). It's some weirder formula.

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We are the carpenters and bricklayers of the Information Age.

Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement.