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

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

Offset: 0

Author

Paul D. Hanna, Oct 14 2005

Keywords

• nonn

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).

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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])}