A125032 Triangle read by rows: T(n,k) = number of tournaments with n players which have the k-th score sequence. The score sequences are in the same order as A068029 and start with the empty score sequence.

1, 1, 2, 6, 2, 24, 8, 8, 24, 120, 40, 40, 120, 40, 120, 240, 280, 24, 720, 240, 240, 720, 240, 720, 1440, 1680, 144, 240, 80, 720, 1440, 2880, 1680, 1680, 1680, 8640, 2400, 144, 2400, 2640, 5040, 1680, 1680, 5040, 1680, 5040, 10080, 11760, 1008, 1680, 560

Offset

1,3

Comments

The score sequences are sorted by number of players and then lexicographically.

There are A000571(m) score sequences for m players. The sum of all the a(n) for m players is A006125(m)=2^(m(m-1)/2).

Links

Martin Fuller, Table of n, a(n) for n = 1..2242

Eric Weisstein's World of Mathematics, Score Sequence

Index entries for sequences related to tournaments

Example

There are two score sequences with 3 players: [0,1,2] from 6 tournaments and [1,1,1] from 2 tournaments. These score sequences come 4th and 5th respectively, so a(4)=6 and a(5)=2.

Crossrefs

Cf. A000571, A006125, A068029, A125031 (number of highest scorers), A123553.

Other sequences that can be calculated using this one: A013976, A125031.

Sequence in context: A320118 A320016 A096485 * A076743 A131980 A217448

Adjacent sequences: A125029 A125030 A125031 * A125033 A125034 A125035

Keyword

nonn,tabf

Author

Martin Fuller, Nov 16 2006

Status

approved