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

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