0,2

Equals column 5 of square table A093729. Also equals column 0 of the matrix 5-th power of triangle A097710, which satisfies the matrix recurrence: A097710(n,k) = [A097710^2](n-1,k-1) + [A097710^2](n-1,k) for n>k>=0.

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

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.

(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])}

Cf. A113077, A113078, A008934, A113089, A113096, A113098, A113100, A113107, A113109, A113111, A113113.

Sequence in context: A090362 A088695 A145166 this_sequence A138427 A005330 A003084

Adjacent sequences: A113076 A113077 A113078 this_sequence A113080 A113081 A113082

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Oct 14 2005