[seqfan] Re: Code

Thu Jun 22 05:43:42 CEST 2017

```Maybe this case is somehow interesting, if so I would love to hear.

But most of the time if I see something like this my first thought is: "this is probably just the output of mashing a few well-known recurrences together, nothing profound."

The following page could be of interest:

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/Fibonomials.html

I had a good laugh over something like this a few years ago. Using polynomial equation definitions of golden ratio it's easy to generate obscenely complicated expressions that always reduce to an algebraic number in Q[sqrt(5)]. You give it to a student or a computer and it thinks forever and ever.

But then there are few guys out there who really understand polynomial division, and they usually can sort out the mess. Utilitarianism aside, that sort of thing is impressive on scholastic grounds alone.

Well, the Sons of Jacob are calling me to watch the online Margaret Atwood videos again, so See ya next time seqfans,

> On Jun 21, 2017, at 10:16 PM, Peter Lawrence <peterl95124 at sbcglobal.net> wrote:
>
> Hans,
>         As I am not familiar with Mathematica (I’m just a C/C++ programmer),
> would it be too much to ask for an explanation of this formula,
> in other words not a proof of its correctness, but rather the details
> of how it computes, what algorithm is being specified here ?
> Are F(n) and F(n+1) inputs, and if so then what is the output, F(n+2) ?
>
> Thanks,
> Peter Lawrence.
>
>
>> On Jun 21, 2017, at 3:51 PM, seqfan-request at list.seqfan.eu wrote:
>>
>> Message: 17
>> Date: Wed, 21 Jun 2017 15:32:01 -0400
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu <mailto:seqfan at list.seqfan.eu>>
>> Subject: [seqfan] Code
>> Message-ID: <C6CC6D76-FE75-4251-ACCC-61CCD0F6C652 at bell.net <mailto:C6CC6D76-FE75-4251-ACCC-61CCD0F6C652 at bell.net>>
>> Content-Type: text/plain; charset=us-ascii
>>
>> I presume that the inclusion of code in sequences is to be able to generate/verify/extend that sequence. Simpler and faster is better. Browsing the OEIS today I chanced upon this Mathematica code for Fibonacci numbers < https://oeis.org/A000045 <https://oeis.org/A000045> >:
>>
>> Table[Fibonacci[n]^5 - Fibonacci[1 + n] + 3 Fibonacci[n]^4 Fibonacci[1 + n] + Fibonacci[n]^3 Fibonacci[1 + n]^2 - 3 Fibonacci[n]^2 Fibonacci[1 + n]^3 - Fibonacci[n] Fibonacci[1 + n]^4 + Fibonacci[1 + n]^5, {n, 1, 10}]
>>
>> It's an interesting Fibonacci identity worthy perhaps of mention in the comments (if it isn't already there) but I'm not sure it ought to be where it is.
>
>
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```