A113079 Number of tournament sequences: a(n) gives the number of n-th generation descendents of a node labeled (5) in the tree of tournament sequences.
1, 5, 40, 515, 10810, 376175, 22099885, 2231417165, 393643922005, 123097221805100, 69087264010363930, 70321483026073531730, 130954011392485408662370, 449450774746306949114288795
Offset: 0
Keywords
Examples
The tree of tournament sequences of descendents of a node labeled (5) begins: [5]; generation 1: 5->[6,7,8,9,10]; generation 2: 6->[7,8,9,10,11,12], 7->[8,9,10,11,12,13,14], 8->[9,10,11,12,13,14,15,16], 9->[10,11,12,13,14,15,16,17,18], 10->[11,12,13,14,15,16,17,18,19,20]; ... 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
Programs
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PARI
{a(n,q=2)=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^q)[r-1,c-1])+(M^q)[r-1,c]))); return((M^5)[n+1,1])}
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