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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 A215207

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 October 22 15:40 EDT 2021. Contains 348172 sequences. (Running on oeis4.)