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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

Can you please compute asymptotic_a[n]-a[n] for a few n and post it here?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Can you please compute asymptotic_a[n]-a[n] for a few n and post it here?

I do not understand that. What is a[n]-a[n]?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
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The first one is asymptotic_a[n], not just a[n].

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Isn't that what the those fractions are in post #98 and 100?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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It is not. Or at least it is not supposed to be. That should be a[n]/asymptotic_a[n].

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Yes, you know what I mean. Okay, I will give the differences.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
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Hm, and what do you get for Floor[asymptotic_a[n]] for different n?

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**bobbym****Administrator**- From: Bumpkinland
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Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Aren't those the sequuence numbers?

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**bobbym****Administrator**- From: Bumpkinland
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Yes, they are.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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So, we have found a simpler exact form?

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**bobbym****Administrator**- From: Bumpkinland
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Yes but with one problem.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

Which?

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**bobbym****Administrator**- From: Bumpkinland
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The floor function is a stepwise function, it is more difficult to work with.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Yes, but at least it is a bit simpler.

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**bobbym****Administrator**- From: Bumpkinland
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Some analytical techniques have problems with anything other than a mathematicians dream like smooth functions. To use them you will have to split the recurrence into 4 of them.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

Which analitycal techniques?

*Last edited by anonimnystefy (2013-04-17 05:59:02)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Almost any of them also some M techniques too.

For instance take a try to find the series coefficient with M, with and without the floor function.

One will fail the other will not.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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