0,3

Equals column 0 of triangle A113095, which satisfies: A113095(n,k) = [A113095^4](n-1,k-1) + [A113095^4](n-1,k).

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

The tree of 4-tournament sequences of descendents

of a node labeled (1) begins:

[1]; generation 1: 1->[4]; generation 2: 4->[7,10,13,16];

generation 3: 7->[10,13,16,19,22,25,28],

10->[13,16,19,22,25,28,31,34,37,40],

13->[16,19,22,25,28,31,34,37,40,43,46,49,52],

16->[19,22,25,28,31,34,37,40,43,46,49,52,55,58,61,64]; ...

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)=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^4)[r-1, c-1])+(M^4)[r-1, c]))); return(M[n+1, 1])}

Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113098, A113100, A113107, A113109, A113111, A113113.

Sequence in context: A000657 A001623 A002077 this_sequence A135078 A107766 A065777

Adjacent sequences: A113093 A113094 A113095 this_sequence A113097 A113098 A113099

nonn

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