A113078 Number of tournament sequences: a(n) gives the number of n-th generation descendents of a node labeled (4) in the tree of tournament sequences.
1, 4, 26, 274, 4721, 134899, 6501536, 537766009, 77598500096, 19821981700354, 9077118324755246, 7531446638893873684, 11423775838657143826346, 31914367054676982206368909, 165251261153335414813452988541
Offset: 0
Keywords
Examples
The tree of tournament sequences of descendents of a node labeled (4) begins: [4]; generation 1: 4->[5,6,7,8]; generation 2: 5->[6,7,8,9,10], 6->[7,8,9,10,11,12], 7->[8,9,10,11,12,13,14], 8->[9,10,11,12,13,14,15,16]; ... 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^4)[n+1,1])}
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