It’s late....but playing with the patterns of squared numbers.
Will post some of what I see tomorrow. Get ready...you know I’m going to ask.
Until then....goodnight allpic.twitter.com/JjtdoQqKgB
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If you add the (n-1)st triangle to the nth square, you get n(3n - 1)/2. But if you add the nth triangle to the nth square, you get n(3n + 1)/2 -- which, remarkably enough, is just (-n)(3(-n) - 1)/2. So one arises from the other by replacing n by -n.
Oh, and by the way, numbers of the form n(3n - 1)/2 are called pentagonal -- for reasons I think you can already see.
Thanks Laurens - I'll think about that.
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