
EXAMPLE

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.


PROG

(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)[r1, c1])+(M^q)[r1, c]))); return((M^5)[n+1, 1])}
