A113098 Number of 4-tournament sequences: a(n) gives the number of increasing sequences of n positive integers (t_1,t_2,...,t_n) such that t_1 = 2 and t_i = 2 (mod 3) and t_{i+1} <= 4*t_i for 1<i<n.

1, 2, 13, 242, 13228, 2241527, 1237069018, 2305369985312, 14874520949557933, 338242806223319079422, 27474512329417917714396073, 8057337874806992183898478061882, 8607002252619465665736907583406214288

Offset

0,2

Comments

Equals column 0 of triangle A113097 = A113095^2 (matrix square), where: A113095(n,k) = [A113095^4](n-1,k-1) + [A113095^4](n-1,k).

Links

Table of n, a(n) for n=0..12.

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

Example

The tree of 4-tournament sequences of descendents
of a node labeled (2) begins:
[2]; generation 1: 2->[5,8]; generation 2:
5->[8,11,14,17,20], 8->[11,14,17,20,23,26,29,32]; ...
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)=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^4)[r-1, c-1])+(M^4)[r-1, c]))); return((M^2)[n+1, 1])}

Crossrefs

Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113100, A113107, A113109, A113111, A113113.

Sequence in context: A268703 A369799 A187648 * A365590 A135870 A133067

Adjacent sequences: A113095 A113096 A113097 * A113099 A113100 A113101

Keyword

nonn

Author

Paul D. Hanna, Oct 14 2005

Status

approved