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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

I verified the results and it seems that:

too. So we get new formula for the stirling numbers!

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

I'll try to generalize the result for higer dimentions.

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Here's analytic definition of p_k (n) in *Mathematica* language:

p := If[#1 == 1, #2(#2 + 1)/2, Sum[i #0[#1 - 1, i], {i, 1, #2}]] &

Example:

p[1,n]=n(n+1)/2

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Strange.

Here's a table of the denominators of p_i (n) for i =1 to 20.

Can someone tell me something about this sequence?

```
2
24
48
5760
11520
11520
2903040
5806080
1393459200
2786918400
367873228800
735746457600
24103053950976000
48206107901952000
578473294823424000
1156946589646848000
9440684171518279680000
18881368343036559360000
271211974879377138647040000
542423949758754277294080000
```

It seems to be very irregular.

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

note that the 5th and 6th term are equal!!!

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Here's more general proposition:

for all natural k,n

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Now I'm veryfing the proposition for n,k <=100. It will take some time.

IPBLE: Increasing Performance By Lowering Expectations.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Ansette wrote:

we have to try and place these individual boxes into a large parcel that must be rectangular with no free space, though the dimensions are irrelevant.. kind of like a three-dimensional tetris..

On the subject of tetris, here's an online game of it: http://www.crazybone.com/onlinegames/li … p?link=232

**igloo** **myrtilles** **fourmis**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Only game???

Where's the maths?

IPBLE: Increasing Performance By Lowering Expectations.

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