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A113111 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 = 3 and t_i = 3 (mod 4) and t_{i+1} <= 5*t_i for 1<i<n. 11
1, 3, 33, 1251, 173505, 94216515, 210576669921, 2002383115518243, 82856383278525698433, 15166287556997012904054915, 12437232461209961704387810340769 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals column 0 of triangle A113110, which is the matrix cube of triangle A113106, which satisfies the recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k).

LINKS

Table of n, a(n) for n=0..10.

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 (3) begins:

[3]; generation 1: 3->[7,11,15];

generation 2: 7->[11,15,19,23,27,31,35],

11->[15,19,23,27,31,35,39,43,47,51,55],

15->[19,23,27,31,35,39,43,47,51,55,59,63,67,71,75]; ...

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^3)[n+1, 1])}

CROSSREFS

Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113100, A113107, A113109, A113113.

Sequence in context: A215948 A012487 A188387 * A118188 A342170 A194889

Adjacent sequences:  A113108 A113109 A113110 * A113112 A113113 A113114

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 14 2005

STATUS

approved

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Last modified January 28 10:49 EST 2022. Contains 350655 sequences. (Running on oeis4.)