A113089 Number of 3-tournament sequences: a(n) gives the number of increasing sequences of n positive integers (t_1,t_2,...,t_n) such that t_1 = 2 and t_i = 2 (mod 2) and t_{i+1} <= 3*t_i for 1<i<n.

1, 2, 10, 114, 2970, 182402, 27392682, 10390564242, 10210795262650, 26494519967902114, 184142934938620227530, 3466516611360924222460082, 178346559667060145108789818842, 25264074391478558474014952210052802

Offset

0,2

Comments

Column 0 of triangle A113088; A113088 is the matrix square of triangle A113084, which satisfies the matrix recurrence: A113084(n,k) = [A113084^3](n-1,k-1) + [A113084^3](n-1,k). Also equals column 2 of square table A113081.

Links

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.

Example

The tree of 3-tournament sequences of even integer
descendents of a node labeled (2) begins:
[2]; generation 1: 2->[4,6];
generation 2: 4->[6,8,10,12], 6->[8,10,12,14,16,18]; ...
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)=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^3)[r-1, c-1])+(M^3)[r-1, c]))); return((M^2)[n+1, 1])}

Crossrefs

Cf. A008934, A113077, A113078, A113079, A113085, A113096, A113098, A113100, A113107, A113109, A113111, A113113.

Sequence in context: A223056 A208782 A237749 * A054928 A132522 A187653

Adjacent sequences: A113086 A113087 A113088 * A113090 A113091 A113092

Keyword

nonn

Author

Paul D. Hanna, Oct 14 2005

Status

approved