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A113107
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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 = 1 and t_i = 1 (mod 4) and t_{i+1} <= 5*t_i for 1<i<n.
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13
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1, 1, 5, 85, 4985, 1082905, 930005021, 3306859233805, 50220281721033905, 3328966349792343354865, 978820270264589718999911669, 1292724512951963810375572954693765
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OFFSET
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0,3
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COMMENTS
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LINKS
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EXAMPLE
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The tree of 5-tournament sequences of descendents
of a node labeled (1) begins:
[1]; generation 1: 1->[5]; generation 2: 5->[9,13,17,21,25]; ...
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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PROG
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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^5)[r-1, c-1])+(M^5)[r-1, c]))); return(M[n+1, 1])}
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CROSSREFS
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Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113100, A113109, A113111, A113113.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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