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 A317723 Round-robin tournament numbers: The number of possible point series for a tournament of n teams playing each other once where n points are awarded to the winning team and 1 to each in the case of a tie. A team winning more games than another always has a higher point score. 1
 1, 2, 7, 40, 367, 4828, 82788, 1750152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The 3-point rule is equivalent to that for football (A064626). The classical 2-point rule is equivalent to that for chess tournaments (A007747). LINKS Table of n, a(n) for n=1..8. Donghwi Park, source code for a(5) EXAMPLE a(1)..a(4) are the same as in A064626. PROG (Python) def play(ps, n, r, i, j): ....if j>=n: ........ps.add(tuple(sorted(r))) ....else: ........(ni, nj) = (i, j+1) if j<(n-1) else (i+1, i+2) ........s=list(r) ........s[i]=r[i]+n; play(ps, n, s, ni, nj) ........s[i]=r[i]+1; s[j]=r[j]+1; play(ps, n, s, ni, nj) ........s[i]=r[i] ; s[j]=r[j]+n; play(ps, n, s, ni, nj) def A317723(n): ....ps=set() ....play(ps, n, [0]*n, 0, 1) ....return len(ps) # Bert Dobbelaere, Oct 07 2018 CROSSREFS Cf. A007747, A064626. Sequence in context: A028441 A006455 A130715 * A340005 A325061 A358745 Adjacent sequences: A317720 A317721 A317722 * A317724 A317725 A317726 KEYWORD nonn,more,hard AUTHOR Donghwi Park, Aug 05 2018 EXTENSIONS a(6)-a(8) from Bert Dobbelaere, Oct 07 2018 STATUS approved

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Last modified August 9 07:48 EDT 2024. Contains 375027 sequences. (Running on oeis4.)