0,2

Column 0 of triangle A113112; A113112 is the matrix 4-th power of triangle A113106, which satisfies the matrix recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k). Also equals column 4 of square table A113103.

T. D. Noe, Table of n, a(n) for n=0..30

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

The tree of 5-tournament sequences of descendents

of a node labeled (4) begins:

[4]; generation 1: 4->[8,12,16,20];

generation 2: 8->[12,16,20,24,28,32,36,40],

12->[16,20,24,28,32,36,40,44,48,52,56,60],

16->[20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80],

20->[24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100];

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^5)[r-1, c-1])+(M^5)[r-1, c]))); return((M^4)[n+1, 1])}

Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113100, A113107, A113109, A113111.

Adjacent sequences: A113110 A113111 A113112 this_sequence A113114 A113115 A113116

Sequence in context: A009105 A091797 A007726 this_sequence A089035 A089516 A000573

nonn

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