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The numbers calculated by the expression:

$$ T(n) = \frac{n(n + 1)}{2} $$

are called Triangular numbers.

What are the numbers (calculated by the expression below) called?

$$ T(n) = \frac{n(n - 1)}{2} $$

Do they have any name at all?

Shaun
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PatrykB
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    Those are exactly the same numbers, just shifted, so that would still be the triangular numbers. – Henrik supports the community Aug 13 '17 at 09:30
  • Thank you, I was suspecting they may be called as "anti triangular numbers" or something like that. I thought they name may differ because those numbers describe the number of entries in the triangular matrix with and without the diagonal. EDIT: if I think about it, well there is no reason to call them differently even thou their connection to the matrices. – PatrykB Aug 13 '17 at 09:36
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    A bit late $$T(n+1) = \frac{(n+1)(n +1 - 1)}{2}=\frac{(n+1)(n)}{2}$$ – James Arathoon Aug 13 '17 at 09:39

1 Answers1

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They're still triangular numbers. Shift by $1$ like so: $n\mapsto n-1$.

Shaun
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