[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
OEIS Classic... I'll ask for advice from Neil Sloane and SeqFan.
See discussion page: [[Talk:Regular orthotopic numbers]]
--
Thanks
Daniel Forgues
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