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A113085
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Number of 3-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 2) and t_{i+1} <= 3*t_i for 1<i<n.
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10
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1, 1, 3, 21, 331, 11973, 1030091, 218626341, 118038692523, 166013096151621, 619176055256353291, 6207997057962300681573, 169117528577725378851523691, 12626174170113987651028630856581, 2602022118010488151483064379958957003
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Equals column 0 of triangle A113084, which satisfies: A113084(n,k) = [A113084^3](n-1,k-1) + [A113084^3](n-1,k).
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LINKS
| M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44.
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EXAMPLE
| The tree of 3-tournament sequences of odd integer
descendents of a node labeled (1) begins:
[1]; generation 1: 1->[3]; generation 2: 3->[5,7,9];
generation 3: 5->[7,9,11,13,15], 7->[9,11,13,15,17,19,21],
9->[11,13,15,17,19,21,23,25,27]; ...
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
| (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^3)[r-1, c-1])+(M^3)[r-1, c]))); return(M[n+1, 1])}
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CROSSREFS
| Cf. A008934, A113077, A113078, A113079, A113089, A113096, A113098, A113100, A113107, A113109, A113111, A113113.
Sequence in context: A134528 A118410 A125054 * A083228 A186271 A101389
Adjacent sequences: A113082 A113083 A113084 * A113086 A113087 A113088
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 14 2005
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