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

1, 2, 16, 440, 43600, 16698560, 26098464448, 172513149018752, 4938593053649344000, 622793203804403960906240, 350552003258337075784341271552, 890153650520295355798989668668129280

Offset: 0

Author

Paul D. Hanna, Oct 14 2005

Keywords

• nonn

Comments

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).

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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])}