A317723 Round-robin tournament numbers: 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 point to each team in the case of a tie. A team winning more games than another always has a higher point score.

1, 2, 7, 40, 367, 4828, 82788, 1750152, 43903333

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).

a(9) = 43903333 was computed by a constraint-based exhaustive enumeration. The computation is empirical but exact: it constructs candidate final standings at the WDL-record level, applies global conservation constraints and canonical ordering, checks realizability, and reproduces all previously listed terms a(1) through a(8). - Muhammed Milani, May 03 2026

Links

Table of n, a(n) for n=1..9.

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: A006455 A130715 A392029 * A392410 A340005 A325061

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

a(9) from Muhammed Milani, May 03 2026

Status

approved