I can never explain it quite to full satisfaction, but before I forget forever:
The difference between successive perfect squares is always the next odd number.
por exemplar: The first six perfect squares are 0...1...4...9...16...25. The difference between 0 and 1 is one, between 1 and 4 is three, between 4 and 9 is five, between 9 and 16 is seven, between 16 and 25 is nine. And so on. 1, 3, 5, 7, 9. Get it?
This from staring intently at a digital clock that read 1:49 a.m. Amazing what a bottle of shiraz, four hours of incessant chatter, and two godawful John Travolta movies will do to the mind.
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