Search: id:A113111
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%I A113111
%S A113111 1,3,33,1251,173505,94216515,210576669921,2002383115518243,
%T A113111 82856383278525698433,15166287556997012904054915,
%U A113111 12437232461209961704387810340769
%N A113111 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 
               = 3 and t_i = 3 (mod 4) and t_{i+1} <= 5*t_i for 1<i<n.
%C A113111 Equals column 0 of triangle A113110, which is the matrix cube of triangle 
               A113106, which satisfies the recurrence: A113106(n,k) = [A113106^5](n-1,
               k-1) + [A113106^5](n-1,k).
%H A113111 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 A113111 The tree of 5-tournament sequences of descendents
%e A113111 of a node labeled (3) begins:
%e A113111 [3]; generation 1: 3->[7,11,15];
%e A113111 generation 2: 7->[11,15,19,23,27,31,35],
%e A113111 11->[15,19,23,27,31,35,39,43,47,51,55],
%e A113111 15->[19,23,27,31,35,39,43,47,51,55,59,63,67,71,75]; ...
%e A113111 Then a(n) gives the number of nodes in generation n.
%e A113111 Also, a(n+1) = sum of labels of nodes in generation n.
%o A113111 (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^3)[n+1,1])}
%Y A113111 Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, 
               A113100, A113107, A113109, A113113.
%Y A113111 Sequence in context: A055549 A086894 A012487 this_sequence A118188 A126675 
               A038694
%Y A113111 Adjacent sequences: A113108 A113109 A113110 this_sequence A113112 A113113 
               A113114
%K A113111 nonn
%O A113111 0,2
%A A113111 Paul D. Hanna (pauldhanna(AT)juno.com), Oct 14 2005

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