cp's OEIS Frontend

A113096 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 = 1 and t_i = 1 (mod 3) and t_{i+1} <= 4*t_i for 1

%I A113096 #5 Mar 30 2012 18:36:51
%S A113096 1,1,4,46,1504,146821,45236404,46002427696,159443238441379,
%T A113096 1926751765436372746,82540801108546193896804,
%U A113096 12696517688186899788062326096,7084402815778394692932546017050054
%N A113096 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 = 1 and t_i = 1 (mod 3) and t_{i+1} <= 4*t_i for 1<i<n.
%C A113096 Equals column 0 of triangle A113095, which satisfies: A113095(n,k) = [A113095^4](n-1,k-1) + [A113095^4](n-1,k).
%H A113096 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 A113096 The tree of 4-tournament sequences of descendents
%e A113096 of a node labeled (1) begins:
%e A113096 [1]; generation 1: 1->[4]; generation 2: 4->[7,10,13,16];
%e A113096 generation 3: 7->[10,13,16,19,22,25,28],
%e A113096 10->[13,16,19,22,25,28,31,34,37,40],
%e A113096 13->[16,19,22,25,28,31,34,37,40,43,46,49,52],
%e A113096 16->[19,22,25,28,31,34,37,40,43,46,49,52,55,58,61,64]; ...
%e A113096 Then a(n) gives the number of nodes in generation n.
%e A113096 Also, a(n+1) = sum of labels of nodes in generation n.
%o A113096 (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[n+1,1])}
%Y A113096 Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113098, A113100, A113107, A113109, A113111, A113113.
%K A113096 nonn
%O A113096 0,3
%A A113096 _Paul D. Hanna_, Oct 14 2005