Author: Andreas Stabel
Date: 00:38:40 01/03/01
Go up one level in this thread
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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