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

Author

Donghwi Park, Aug 05 2018

Keywords

• nonn
• more
• hard

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).

Examples

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

Links

• Donghwi Park, source code for a(5)

Crossrefs

Cf. A007747, A064626.

Programs

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

Extensions

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