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Search: id:A113100
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| A113100 |
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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 = 3 and t_i = 3 (mod 3) and t_{i+1} <= 4*t_i for 1<i<n. |
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+0
14
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| 1, 3, 27, 693, 52812, 12628008, 9924266772, 26507035453923, 246323730279500082, 8100479557816637139288, 954983717308947379891713642, 407790020849346203244152231395953
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Column 0 of triangle A113099; A113099 is the matrix cube of triangle A113095, which satisfies the matrix recurrence: A113095(n,k) = [A113095^4](n-1,k-1) + [A113095^4](n-1,k). Also equals column 3 of square table A113092.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..30
M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44.
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EXAMPLE
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The tree of 4-tournament sequences of descendents of a node labeled (3) begins:
[3]; generation 1: 3->[6,9,12]; generation 2:
6->[9,12,15,18,21,24], 9->[12,15,18,21,24,27,30,33,36],
12->[15,18,21,24,27,30,33,36,39,42,45,48]; ...
Then a(n) gives the number of nodes in generation n.
Also, a(n+1) = sum of labels of nodes in generation n.
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PROGRAM
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(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^3)[n+1, 1])}
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CROSSREFS
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Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113107, A113109, A113111, A113113.
Sequence in context: A062496 A099084 A085656 this_sequence A038379 A047656 A052269
Adjacent sequences: A113097 A113098 A113099 this_sequence A113101 A113102 A113103
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 14 2005
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