A113080 - OEIS

%I #4 Mar 30 2012 18:36:51

%S 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,

%T 0,6377,182402,52812,2704,100,6,1,0,171886,27392682,12628008,481376,

%U 8125,162,7,1,0,7892642,10390564242,9924266772,337587520,2918750,20502,245,8

%N 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.

%C 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.

%H M. Cook and M. Kleber, <a href="http://www.combinatorics.org/Volume_7/Abstracts/v7i1r44.html">Tournament sequences and Meeussen sequences</a>, Electronic J. Comb. 7 (2000), #R44.

%e Table begins:

%e 1,1,1,1,1,1,1,1,1,1,1,1,1,...

%e 0,1,2,3,4,5,6,7,8,9,10,11,...

%e 0,2,10,27,56,100,162,245,352,486,650,...

%e 0,7,114,693,2704,8125,20502,45619,92288,173259,...

%e 0,41,2970,52812,481376,2918750,13399506,50216915,...

%e 0,397,182402,12628008,337587520,4976321250,48633051942,...

%e 0,6377,27392682,9924266772,978162377600,42197834315625,...

%e 0,171886,10390564242,26507035453923,12088945462984960,...

%e 0,7892642,10210795262650,246323730279500082,...

%o (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])}

%Y 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).

%K nonn,tabl

%O 1,8

%A _Paul D. Hanna_, Oct 14 2005