[seqfan] Re: A025597 computation

[David Wilson]

Wouter picked up on a couple of mistakes in my posting, which I acknowledge.

The point being, Wouter's computations matched my own, which I believe 
to be correct (for what that's worth), and RGWv's computations differed 
by 1 in two terms, in the direction expected due to roundoff/truncation 
errors.

I have added the formula to A025597 and Wouter's terms to the b-file, 
these await editorial approval.

On 6/24/2012 4:37 PM, Wouter Meeussen wrote:
> David,
>
> here you reversed them:
>> Specifically, for a(10) Wouter and I have 20369 while RGWv has 20370.
> we had 20370 and RGWv had 20369
>
> here you mislabeled them
>> At a(26) Wouter has 2083200939963715126 while RGWv has 
>> 2083200939963715125.
> you show  a(25)
>
> and only then does your correct remark "In both cases, RGWv's value is 
> 1 smaller" fit the data.
> But isn't it a surprising formula for counting kings' paths (more like 
> walks actually, his Majesty doesn't seem te be in a hurry)?
> I've never seen anything like it!
>
> W.
>
> -----Original Message----- From: David Wilson
> Sent: Sunday, June 24, 2012 10:13 PM
> To: Sequence Fanatics
> Subject: [seqfan] Re: A025597 computation
>
> Thanks to those who helped me test this formula.
>
> I am confident that the values I submitted for A025597 were correct.
> They were computed using integer arithmetic.
>
> Ed Jeffrey verified that the formula agrees with my terms.
>
> Wouter Meeussen's formula computations also verify my terms.
>
> RGWv's computations disagree with mine at a couple of points.
> Specifically, for a(10) Wouter and I have 20369 while RGWv has 20370. At
> a(26) Wouter has 2083200939963715126 while RGWv has 2083200939963715125.
> In both cases, RGWv's value is 1 smaller, which I would expect from
> truncation of slightly low near-integer real values.
>
> So I am going accept the formula as accurate and add it to A025597, and
> I will also add Wouter's extension.
>
> Again, thanks for the help.
>
> - Dave Wilson
>
>
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