A113078 Number of tournament sequences: a(n) gives the number of n-th generation descendents of a node labeled (4) in the tree of tournament sequences.

1, 4, 26, 274, 4721, 134899, 6501536, 537766009, 77598500096, 19821981700354, 9077118324755246, 7531446638893873684, 11423775838657143826346, 31914367054676982206368909, 165251261153335414813452988541

Offset

0,2

Comments

Equals column 4 of square table A093729. Also equals column 0 of the matrix 4th power of triangle A097710, which satisfies the matrix recurrence: A097710(n,k) = [A097710^2](n-1,k-1) + [A097710^2](n-1,k) for n>k>=0.

Links

Table of n, a(n) for n=0..14.

M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44.

Example

The tree of tournament sequences of descendents of a node labeled (4) begins:
[4]; generation 1: 4->[5,6,7,8]; generation 2: 5->[6,7,8,9,10],
6->[7,8,9,10,11,12], 7->[8,9,10,11,12,13,14],
8->[9,10,11,12,13,14,15,16]; ...
Then a(n) gives the number of nodes in generation n.
Also, a(n+1) = sum of labels of nodes in generation n.

Prog

(PARI) {a(n, q=2)=local(M=matrix(n+1, n+1)); for(r=1, n+1, for(c=1, r, M[r, c]=if(r==c, 1, if(c>1, (M^q)[r-1, c-1])+(M^q)[r-1, c]))); return((M^4)[n+1, 1])}

Crossrefs

Cf. A113077, A113079, A008934, A113089, A113096, A113098, A113100, A113107, A113109, A113111, A113113.

Sequence in context: A248668 A079473 A145164 * A177451 A304864 A167811

Adjacent sequences: A113075 A113076 A113077 * A113079 A113080 A113081

Keyword

nonn

Author

Paul D. Hanna, Oct 14 2005

Status

approved