cp's OEIS Frontend

A113085 Number of 3-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 2) and t_{i+1} <= 3*t_i for 1

%I A113085 #5 Mar 30 2012 18:36:51
%S A113085 1,1,3,21,331,11973,1030091,218626341,118038692523,166013096151621,
%T A113085 619176055256353291,6207997057962300681573,
%U A113085 169117528577725378851523691,12626174170113987651028630856581,2602022118010488151483064379958957003
%N A113085 Number of 3-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 2) and t_{i+1} <= 3*t_i for 1<i<n.
%C A113085 Equals column 0 of triangle A113084, which satisfies: A113084(n,k) = [A113084^3](n-1,k-1) + [A113084^3](n-1,k).
%H A113085 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 A113085 The tree of 3-tournament sequences of odd integer
%e A113085 descendents of a node labeled (1) begins:
%e A113085 [1]; generation 1: 1->[3]; generation 2: 3->[5,7,9];
%e A113085 generation 3: 5->[7,9,11,13,15], 7->[9,11,13,15,17,19,21],
%e A113085 9->[11,13,15,17,19,21,23,25,27]; ...
%e A113085 Then a(n) gives the number of nodes in generation n.
%e A113085 Also, a(n+1) = sum of labels of nodes in generation n.
%o A113085 (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^3)[r-1,c-1])+(M^3)[r-1,c]))); return(M[n+1,1])}
%Y A113085 Cf. A008934, A113077, A113078, A113079, A113089, A113096, A113098, A113100, A113107, A113109, A113111, A113113.
%K A113085 nonn
%O A113085 0,3
%A A113085 _Paul D. Hanna_, Oct 14 2005