cp's OEIS Frontend

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 A113098 #5 Mar 30 2012 18:36:51
%S A113098 1,2,13,242,13228,2241527,1237069018,2305369985312,14874520949557933,
%T A113098 338242806223319079422,27474512329417917714396073,
%U A113098 8057337874806992183898478061882,8607002252619465665736907583406214288
%N 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.
%C A113098 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).
%H A113098 M. Cook and M. Kleber, <a href="http://www.combinatorics.org/Volume_7/Abstracts/v7i1r44.html">Tournament sequences and Meeussen sequences</a>, Electronic J. Comb. 7 (2000), #R44.
%e A113098 The tree of 4-tournament sequences of descendents
%e A113098 of a node labeled (2) begins:
%e A113098 [2]; generation 1: 2->[5,8]; generation 2:
%e A113098 5->[8,11,14,17,20], 8->[11,14,17,20,23,26,29,32]; ...
%e A113098 Then a(n) gives the number of nodes in generation n.
%e A113098 Also, a(n+1) = sum of labels of nodes in generation n.
%o A113098 (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])}
%Y A113098 Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113100, A113107, A113109, A113111, A113113.
%K A113098 nonn
%O A113098 0,2
%A A113098 _Paul D. Hanna_, Oct 14 2005