A113080 Square table, read by antidiagonals, where T(n,k) equals the number of k-tournament sequences of length n for k>=1, with T(0,k) = 1 for k>=1 and T(n,1) = 0 for n>0.

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 7, 10, 3, 1, 0, 41, 114, 27, 4, 1, 0, 397, 2970, 693, 56, 5, 1, 0, 6377, 182402, 52812, 2704, 100, 6, 1, 0, 171886, 27392682, 12628008, 481376, 8125, 162, 7, 1, 0, 7892642, 10390564242, 9924266772, 337587520, 2918750, 20502, 245, 8

Offset: 1

Author

Paul D. Hanna, Oct 14 2005

Keywords

• nonn
• tabl

Comments

A k-tournament sequence is an increasing sequence of positive integers (t_1,t_2,...) such that t_1 = p, t_i = p (mod k-1) and t_{i+1} <= k*t_i, where k>1, p>=1. This is the table of k-tournament sequences when the starting node has label p = 1 for k>=1.

Examples

			Table begins:
1,1,1,1,1,1,1,1,1,1,1,1,1,...
0,1,2,3,4,5,6,7,8,9,10,11,...
0,2,10,27,56,100,162,245,352,486,650,...
0,7,114,693,2704,8125,20502,45619,92288,173259,...
0,41,2970,52812,481376,2918750,13399506,50216915,...
0,397,182402,12628008,337587520,4976321250,48633051942,...
0,6377,27392682,9924266772,978162377600,42197834315625,...
0,171886,10390564242,26507035453923,12088945462984960,...
0,7892642,10210795262650,246323730279500082,...
		

Links

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

Crossrefs

Columns: A008934 (k=2), A113089 (k=3), A113100 (k=4), A113113 (k=5); related tables: A093729 (k=2), A113081 (k=3), A113092 (k=4), A113103 (k=5).

Programs

PARI

{T(n,k)=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^k)[r-1,c-1])+(M^k)[r-1,c]))); return((M^(k-1))[n+1,1])}