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%I #5 Mar 30 2012 18:36:51
%S 1,2,16,440,43600,16698560,26098464448,172513149018752,
%T 4938593053649344000,622793203804403960906240,
%U 350552003258337075784341271552,890153650520295355798989668668129280
%N Number of 5-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 4) and t_{i+1} <= 5*t_i for 1<i<n.
%C Equals column 0 of triangle A113108, which is the matrix square of triangle A113106, which satisfies the recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k).
%H 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 The tree of 5-tournament sequences of descendents
%e of a node labeled (2) begins:
%e [2]; generation 1: 2->[6,10]; generation 2:
%e 6->[10,14,18,22,26,30], 10->[14,18,22,26,30,34,38,42,46,50]; ...
%e Then a(n) gives the number of nodes in generation n.
%e Also, a(n+1) = sum of labels of nodes in generation n.
%o (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^5)[r-1,c-1])+(M^5)[r-1,c]))); return((M^2)[n+1,1])}
%Y Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113100, A113107, A113111, A113113.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 14 2005
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