A007747 -id:A007747 - cp's OEIS frontend

A047734 Number of score sequences in tournament with n players, when 7 points are awarded in each game.

1, 4, 32, 318, 3692, 47536, 657040, 9563961, 144847330, 2263567060, 36281911266, 593856894136, 9892591942306, 167278802007062, 2865331941321996, 49634901816988932, 868329574365547207

Offset: 1

David W. Wilson

nonn

Qihao Ye, Table of n, a(n) for n = 1..770

Cf. A000571, A007747, A047729-A047731.

Nonnegative integer points (p_1, p_2, ..., p_n) in polytope p_0=p_{n+1}=0, 2p_i -(p_{i+1}+p_{i-1}) <= 7, p_i >= 0, i=1, ..., n.

A047735 Number of score sequences in tournament with n players, when 8 points are awarded in each game.

Original entry on oeis.org

1, 5, 41, 459, 6033, 88055, 1379405, 22763356, 390859501, 6924877318, 125837754305, 2335060741480, 44097660919285, 845336236860344, 16415016380975679, 322349248087651458, 6392828942756895663

Offset: 1

David W. Wilson

nonn

Qihao Ye, Table of n, a(n) for n = 1..739

Cf. A000571, A007747, A047729, A047730, A047731.

Nonnegative integer points (p_1, p_2, ..., p_n) in polytope p_0=p_{n+1}=0, 2p_i -(p_{i+1}+p_{i-1}) <= 8, p_i >= 0, i=1, ..., n.

A047736 Number of score sequences in tournament with n players, when 9 points are awarded in each game.

Original entry on oeis.org

1, 5, 50, 630, 9285, 151652, 2658131, 49061128, 942055396, 18662965393, 379195887105, 7867076520341, 166102773740621, 3559787677138284, 77278541685154409, 1696519572528877274

Offset: 1

David W. Wilson

nonn

Qihao Ye, Table of n, a(n) for n = 1..714

Cf. A000571, A007747, A047729, A047730, A047731.

Nonnegative integer points (p_1, p_2, ..., p_n) in polytope p_0=p_{n+1}=0, 2p_i -(p_{i+1}+p_{i-1}) <= 9, p_i >= 0, i=1, ..., n.

A047737 Number of score sequences in tournament with n players, when 10 points are awarded in each game.

Original entry on oeis.org

1, 6, 61, 846, 13771, 248623, 4816659, 98277943, 2086173336, 45688601782, 1026218795502, 23536101285148, 549336702455778, 13014352354398322, 312313455482385108, 7579157833713922471

Offset: 1

David W. Wilson

nonn

Qihao Ye, Table of n, a(n) for n = 1..692

Cf. A000571, A007747, A047729, A047730, A047731.

Nonnegative integer points (p_1, p_2, ..., p_n) in polytope p_0 = p_{n+1} = 0, 2*p_i - (p_{i+1} + p_{i-1}) <= 10, p_i >= 0, i = 1..n.

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.

Original entry on oeis.org

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

Offset: 1

Donghwi Park, Aug 05 2018

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(1)..a(4) are the same as in A064626.

Donghwi Park, source code for a(5)

Cf. A007747, A064626.

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

a(6)-a(8) from Bert Dobbelaere, Oct 07 2018

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A047734 Number of score sequences in tournament with n players, when 7 points are awarded in each game.

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A047735 Number of score sequences in tournament with n players, when 8 points are awarded in each game.

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A047736 Number of score sequences in tournament with n players, when 9 points are awarded in each game.

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A047737 Number of score sequences in tournament with n players, when 10 points are awarded in each game.

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Author

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Formula

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.

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