[seqfan] Re: 0^n in A097135
Alonso Del Arte
alonso.delarte at gmail.com
Sun Jan 24 00:59:39 CET 2010
Yes, F(n) stands for the Fibonacci numbers. I was unaware of A7, and I'm not
sure I agree with its definition. However, my assertion that 0^0 is
indeterminate comes not from any deep mathematical understanding on my part,
but was simply my repeating what Mathematica told me.
Given that a(n) = 3F(n) starting with a(0) is already in the OEIS as
A022086, it is perhaps not so concerning that the definition of A097135 is
needlessly complicated by the distraction of 0^0.
On Fri, Jan 22, 2010 at 8:14 PM, Robert Munafo <mrob27 at gmail.com> wrote:
> 0^n is A000007, and "F(n)" seems to imply the Fibonacci numbers, so I
> suggest defining A097135 as "3*A000045(n)+A000007(n)".
> On Fri, Jan 22, 2010 at 19:56, Alonso Del Arte <alonso.delarte at gmail.com
> > I'm not sure I understand what's the point of 0^n in the definition of
> > A097135. For n < 0 it's complex infinity, for n = 0 it's indeterminate,
> > for n > 0 it's just 0. I am aware that there are some calculators that
> > give 0^0 = 1 (we've probably discused that in this list), but even if we
> > agreed that's the proper definition, it might perhaps be more
> > straightforward to define the sequence as a(n) = 3F_n with the arbitrary
> > assignment a(0) = 1. Or change a(0) to 0 or maybe drop a(0) altogether.
> Robert Munafo -- mrob.com
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