# chess tournaments:

Svante Linusson linusson at matematik.su.se
Wed Apr 28 17:44:03 CEST 1999

```>We can parameterize these sequences on the total number of pointsp awarded
>per game.  In such a game, there are p+1
>possible game
>outcomes, namely (0,p), (1,p-1), ..., and (p,0).  Let A_p(n) count
>the number of score sequences for n players for n = 1, 2, 3, ....
>
>The A047657 = A_2, and your other requested sequence is A_3.
>I have computed the first few values for A_p, for 1 <= p <= 5.
>
>p       A_p
>
>1       1,1,2,4,9,22,59,167,490,1486
>2       1,2,5,16,59,247,1111,5302,26376
>3       1,2,8,37,198,1178,7548
>4       1,3,13,76,521,3996,32923
>5       1,3,18,131,1111,10461
>
>Notes:
>
>    A047657 should be indexed starting at 1.
>    A_1 is probably the same as A000571.  Whereas A_1 has a recurrence,
>        it might be possible to work one out for all A_p.
>    A_2 is probably the same as A007747.

By changing <=2 in the description of A007747 to <=p, you should get the
same sequences.

/Svante

=========================================================
Svante Linusson
Matematiska Institutionen	tel. 08-16 14 34
Stockholms Universitet		fax. 08-612 67 17
S-10691 Stockholm		linusson at matematik.su.se
SWEDEN

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