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Subject: Re: Distinct position enumeration

Author: Heiner Marxen

Date: 14:05:13 01/02/01

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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



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