A113077 Column 3 of square table A093729; a(n) gives the number of n-th generation descendents of a node labeled (3) in the tree of tournament sequences, for n>=0.

1, 3, 15, 123, 1656, 36987, 1391106, 89574978, 10036638270, 1986129275673, 703168200003336, 450303519404234922, 526421174510139860241, 1132076561237754405471033, 4507472672071759672232970720

Offset

0,2

Comments

Also equals column 0 of the matrix cube 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.

Links

Table of n, a(n) for n=0..14.

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

Example

The tree of tournament sequences of descendents of a node labeled (3) begins:
[3]; generation 1: 3->[4,5,6]; generation 2: 4->[5,6,7,8],
5->[6,7,8,9,10], 6->[7,8,9,10,11,12]; ...
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)[r-1, c-1])+(M^q)[r-1, c]))); return((M^3)[n+1, 1])}

Crossrefs

Cf. A113078, A113079.

Sequence in context: A197505 A348903 A191371 * A251661 A230657 A246573

Adjacent sequences: A113074 A113075 A113076 * A113078 A113079 A113080

Keyword

nonn

Author

Paul D. Hanna, Oct 14 2005

Status

approved