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Search: id:A113077
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| A113077 |
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Column 3 of square table A093729; a(n) gives the number of n-th generation descendents of a node labeled (3) in the tree of tournament sequences, for n>=0. |
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+0
12
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| 1, 3, 15, 123, 1656, 36987, 1391106, 89574978, 10036638270, 1986129275673, 703168200003336, 450303519404234922, 526421174510139860241, 1132076561237754405471033, 4507472672071759672232970720
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also equals column 0 of the matrix cube of triangle A097710, which satisfies the matrix recurrence: A097710(n,k) = [A097710^2](n-1,k-1) + [A097710^2](n-1,k) for n>k>=0.
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LINKS
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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 tournament sequences of descendents of
a node labeled (3) begins:
[3]; generation 1: 3->[4,5,6]; generation 2: 4->[5,6,7,8],
5->[6,7,8,9,10], 6->[7,8,9,10,11,12]; ...
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, q=2)=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^q)[r-1, c-1])+(M^q)[r-1, c]))); return((M^3)[n+1, 1])}
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CROSSREFS
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Cf. A113078, A113079.
Adjacent sequences: A113074 A113075 A113076 this_sequence A113078 A113079 A113080
Sequence in context: A093571 A093570 A107869 this_sequence A135255 A075475 A074241
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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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