cp's OEIS Frontend

A113107 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 = 1 and t_i = 1 (mod 4) and t_{i+1} <= 5*t_i for 1

%I A113107 #7 Mar 13 2015 22:32:33
%S A113107 1,1,5,85,4985,1082905,930005021,3306859233805,50220281721033905,
%T A113107 3328966349792343354865,978820270264589718999911669,
%U A113107 1292724512951963810375572954693765
%N A113107 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 = 1 and t_i = 1 (mod 4) and t_{i+1} <= 5*t_i for 1<i<n.
%C A113107 Equals column 0 of triangle A113106 which satisfies recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k), where A113106^5 is the matrix 5th power.
%H A113107 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 A113107 The tree of 5-tournament sequences of descendents
%e A113107 of a node labeled (1) begins:
%e A113107 [1]; generation 1: 1->[5]; generation 2: 5->[9,13,17,21,25]; ...
%e A113107 Then a(n) gives the number of nodes in generation n.
%e A113107 Also, a(n+1) = sum of labels of nodes in generation n.
%o A113107 (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[n+1,1])}
%Y A113107 Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113100, A113109, A113111, A113113.
%K A113107 nonn
%O A113107 0,3
%A A113107 _Paul D. Hanna_, Oct 14 2005