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

1, 3, 33, 1251, 173505, 94216515, 210576669921, 2002383115518243, 82856383278525698433, 15166287556997012904054915, 12437232461209961704387810340769

Offset: 0

Author

Paul D. Hanna, Oct 14 2005

Keywords

• nonn

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).

Examples

			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.
		

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, A113109, 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^3)[n+1,1])}