0,3

The number of outcomes of chess tournament with n players.

For n >= 1 a(n) is the size of the Sylow 3-subgroup of the Chevalley group A_n(3) (sequence A053290). - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 30 2001

The number of binary relations on an n-element set that are both reflexive and antisymmetric. - Justin Witt (justinmwitt(AT)gmail.com), Jul 12 2005

The sequence a(n+1)= [1,3,27,729,59049,14348907,...] is the Hankel transform (see A001906 for definition) of A047891 = 1, 3, 12, 57, 300, 1586, 9912, .., . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 29 2006

a(n) is the number of binary relations on a set with n elements that are total relations, i.e. for a relation on a set X it holds for all a and b in X that a~b or b~a (or both). E.g. a(2)= 3 because there are three total relations on a set with two elements: {(a,a),(a,b),(b,a),(b,b)}, {(a,a),(a,b),(b,a)}, {(a,b),(b,a),(b,b)} - Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), May 23 2008

P. A. MacMahon, Chess tournaments and the like treated by the calculus of symmetric functions, Coll. Papers I, MIT Press, 344-375.

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.

Index entries for sequences related to tournaments

a(n+1) is the determinant of n X n matrix M_(i, j)=binomial(3*i, j) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 27 2003

Sequence is given by the Hankel transform (see A001906 for definition) of A007564 = {1, 1, 4, 19, 100, 562, 3304, ...}; example : det([1, 1, 4, 19; 1, 4, 19, 100; 4, 19, 100, 562; 19, 100, 562, 3304]) = 3^6 = 729 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 20 2005

The sequence a(n+1)= [1,3,27,729,59049,14348907,...] is the Hankel transform (see A001906 for definition) of A047891 = 1, 3, 12, 57, 300, 1586, 9912, .., . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 29 2006

a(n)=3^(C(2+n,n)), n>=-2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2007

seq(3^(binomial(2+n, n)), n=-2..12); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2007

a:=n->mul (3^j, j=1..n): seq(a(n), n=-1..13); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 03 2007

with(finance):seq(mul(futurevalue( 1, 2, k), k=0..n), n=-1..13); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 01 2008

Cf. A007747.

Sequence in context: A085656 A113100 A038379 this_sequence A052269 A138525 A012505

Adjacent sequences: A047653 A047654 A047655 this_sequence A047657 A047658 A047659

nonn

N. J. A. Sloane (njas(AT)research.att.com).