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A113113
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 = 4 and t_i = 4 (mod 4) and t_{i+1} <= 5*t_i for 1<i<n.
14
1, 4, 56, 2704, 481376, 337587520, 978162377600, 12088945462984960, 651451173346940188160, 155573037664478034394215424, 166729581953452524706695313356800
OFFSET
0,2
COMMENTS
Column 0 of triangle A113112; A113112 is the matrix 4th power of triangle A113106, which satisfies the matrix recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k). Also equals column 4 of square table A113103.
LINKS
M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44.
EXAMPLE
The tree of 5-tournament sequences of descendents
of a node labeled (4) begins:
[4]; generation 1: 4->[8,12,16,20];
generation 2: 8->[12,16,20,24,28,32,36,40],
12->[16,20,24,28,32,36,40,44,48,52,56,60],
16->[20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80],
20->[24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100];
Then a(n) gives the number of nodes in generation n.
Also, a(n+1) = sum of labels of nodes in generation n.
PROG
(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^4)[n+1, 1])}
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 14 2005
STATUS
approved