A330637 Number of n-team football tournament outcomes that can be obtained in a single way. Each team plays each other team once, where 3 points are awarded to the winning team and 1 to each team in the case of a draw.

1, 2, 6, 25, 106, 436, 1795, 7487

Offset: 1

Author

Dmitry Kamenetsky, Dec 22 2019

Keywords

• nonn
• more
• hard

Comments

Since such outcomes are obtained in a single way, their individual games can be uniquely reconstructed. This allows them to be used in a reconstruction puzzle (see links).

Examples

			For 2 teams there are 2 outcomes that can be obtained in a single way: [0, 3] and [1, 1], so a(2) = 2.
For 3 teams there are 6 outcomes that can be obtained in a single way: [0, 3, 6], [1, 3, 4], [1, 1, 6], [1, 2, 4], [0, 4, 4] and [2, 2, 2], so a(3) is 6. Note that the outcome [3, 3, 3] can be obtained in two ways: (A beats B, B beats C, C beats A) or (B beats A, A beats C, C beats B).
		

Links

• Dmitry Kamenetsky, Reconstructing the results of a 5-team soccer tournament, Puzzling StackExchange, 2019.
• Dmitry Kamenetsky, Reconstructing the results of a 6-team soccer tournament, Puzzling StackExchange, 2019.

Crossrefs

Cf. A064626 counts all outcomes.

Extensions

a(7) from Giovanni Resta, Jan 02 2020

a(8) from Andrew Howroyd, Feb 28 2020