# [seqfan] "Start a sequence at the earliest reasonable point, but no earlier."

Daniel Forgues kephalopod at gmail.com
Thu Jul 29 00:50:15 CEST 2010

```About the starting point of figurate numbers and centered figurate
numbers (Cf. [[:Category:Figurate numbers]])

I observed throughout OEIS and MathWorld that the convention for
figurate numbers is that it is 0 for n = 0 and 1 (initial dot) for n =
1 while the convention for GLOBALLY (e.g. "centered" pyramidal numbers
are NOT globally centered, it is only a stacking of centered polygons
and starts at 0 for n = 0 since it does not have a global central dot)
centered figurate numbers is to have the central dot, giving 1, for n
= 0.

In the OEIS, the figurate numbers sequences authored by Neil Sloane
typically start at n = 0 giving 0 followed by n = 1 giving 1, while
the GLOBALLY centered figurate numbers start at n = 0 giving 1 for the
mandatory central dot. Sequences authored by other people do not
always follow that convention. That convention seems the most common.
It seems to me that to always have 1 (the initial dot for figurate
numbers; the globally central dot for GLOBALLY centered figurate
numbers) for n = 0 would have been a better convention since n would
then correspond to the number of nondegenerate subfigures.

Just check the OEIS sequences of figurate numbers and GLOBALLY
centered figurate numbers, especially the ones authored by Neil
Sloane. (Cf. [[Polygonal numbers]] and [[Platonic numbers]], among
other figurate numbers)

Since most figurate numbers sequences in the OEIS start with 0 for n =
0 (while the globally centered figurate numbers starting with 1 for n
= 0) I made the sequences in the wiki to abide by the same. I feel
like leaving it as it is for now and ask for advice from Neil Sloane
and other people before removing all entries for n = 0 for the not
globally centered figurate numbers (I don't want to be told later that
I should not have removed those and to have to put them all back
again...) Removing them would make the wiki less consistent with the

See discussion page: [[Talk:Regular orthotopic numbers]]

--

Thanks

Daniel Forgues

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