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A113109 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 = 2 and t_i = 2 (mod 4) and t_{i+1} <= 5*t_i for 1<i<n. 11
1, 2, 16, 440, 43600, 16698560, 26098464448, 172513149018752, 4938593053649344000, 622793203804403960906240, 350552003258337075784341271552, 890153650520295355798989668668129280 (list; graph; refs; listen; history; text; internal format)



Equals column 0 of triangle A113108, which is the matrix square of triangle A113106, which satisfies the recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k).


Table of n, a(n) for n=0..11.

M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44.


The tree of 5-tournament sequences of descendents

of a node labeled (2) begins:

[2]; generation 1: 2->[6,10]; generation 2:

6->[10,14,18,22,26,30], 10->[14,18,22,26,30,34,38,42,46,50]; ...

Then a(n) gives the number of nodes in generation n.

Also, a(n+1) = sum of labels of nodes in generation n.


(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^2)[n+1, 1])}


Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113100, A113107, A113111, A113113.

Sequence in context: A012682 A012678 A012146 * A223563 A140309 A201383

Adjacent sequences:  A113106 A113107 A113108 * A113110 A113111 A113112




Paul D. Hanna, Oct 14 2005



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Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)