

A113100


Number of 4tournament 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.


14



1, 3, 27, 693, 52812, 12628008, 9924266772, 26507035453923, 246323730279500082, 8100479557816637139288, 954983717308947379891713642, 407790020849346203244152231395953
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OFFSET

0,2


COMMENTS

Column 0 of triangle A113099; A113099 is the matrix cube of triangle A113095, which satisfies the matrix recurrence: A113095(n,k) = [A113095^4](n1,k1) + [A113095^4](n1,k). Also equals column 3 of square table A113092.


LINKS

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.


EXAMPLE

The tree of 4tournament 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.


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^4)[r1, c1])+(M^4)[r1, c]))); return((M^3)[n+1, 1])}


CROSSREFS

Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113107, A113109, A113111, A113113.
Sequence in context: A185237 A099084 A085656 * A038379 A047656 A193610
Adjacent sequences: A113097 A113098 A113099 * A113101 A113102 A113103


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Oct 14 2005


STATUS

approved



