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Subject: Re: Distinct position enumeration

Author: Andreas Stabel

Date: 00:38:40 01/03/01

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On January 02, 2001 at 17:05:13, Heiner Marxen wrote:

>On January 02, 2001 at 04:45:47, Andreas Stabel wrote:
>
>>On December 29, 2000 at 10:26:06, Steven J. Edwards wrote:
>>
>>>Briefly, I have calculated the number of distinct positions after N ply for N
>>>equals zero upto nine.  Can someone extend this series, or has anyone already
>>>done so?
>>>
>>>1,20,400,5362,72078,822518,9417683
>>>
>>>See:
>>>
>>>http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=057745
>>>
>>>-- Steven
>>>
>>>chessnotation@earthlink.net
>>
>>I have earlier posted the following table which, unfortunately, does not
>>match your numbers after ply 3.
>>
>>Table from opening position:
>>   |               | Unique nodes  | Unique nodes II Unique nodes  | Factor |
>>Ply| Total # nodes | ep = pawn two | ep = oppositeII ep = Only if  | prev.  |
>>   |               |               | pawn can hit II ep is legal   | row    |
>>---+---------------+---------------+--------------II---------------+--------|
>> 0 |             1 |             1 |            1 II             1 |        |
>> 1 |            21 |            21 |           21 II            21 |  21.00 |
>> 2 |           421 |           421 |          421 II           421 |  20.05 |
>> 3 |          9323 |          8023 |         5783 II          5783 |  13.74 |
>> 4 |        206604 |        109262 |        77796 II         77796 |  13.45 |
>> 5 |       5072213 |       1351950 |       898812 II        898812 |  11.55 |
>> 6 |     124132537 |      15334851 |     10281864 II      10281862 |  11.44 |
>> 7 |    3320034397 |     160373323 |    106193912 II     106193643 |  10.33 |
>> 8 |   88319013353 |               |              II               |        |
>> 9 | 2527849247520 |               |              II               |        |
>>
>>
>>Best regards
>>Andreas Stabel
>
>Andreas, obviously you are summung up the numbers of Steven, i.e.
>  21 = 1+20
> 421 = 1+20+400
>5783 = 1+20+400+5362
>I did not check further.  (column opposite pawn can hit)
>
>Heiner

Unfortunately you are wrong :)
As you see from my comment above, I said that after ply 3 our numbers don't
match. F.ex. your ply 4 gives 1+20+400+5362+72078 = 77861, and my number
is 77796. It would be interresting to find out what is the correct numbers.

Regards
Andreas Stabel



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