A113085 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 = 1 and t_i = 1 (mod 2) and t_{i+1} <= 3*t_i for 1<i<n.

1, 1, 3, 21, 331, 11973, 1030091, 218626341, 118038692523, 166013096151621, 619176055256353291, 6207997057962300681573, 169117528577725378851523691, 12626174170113987651028630856581, 2602022118010488151483064379958957003

Offset

0,3

Comments

Equals column 0 of triangle A113084, which satisfies: A113084(n,k) = [A113084^3](n-1,k-1) + [A113084^3](n-1,k).

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 3-tournament sequences of odd integer
descendents of a node labeled (1) begins:
[1]; generation 1: 1->[3]; generation 2: 3->[5,7,9];
generation 3: 5->[7,9,11,13,15], 7->[9,11,13,15,17,19,21],
9->[11,13,15,17,19,21,23,25,27]; ...
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[n+1, 1])}

Crossrefs

Cf. A008934, A113077, A113078, A113079, A113089, A113096, A113098, A113100, A113107, A113109, A113111, A113113.

Sequence in context: A332974 A118410 A125054 * A240936 A342245 A332928

Adjacent sequences: A113082 A113083 A113084 * A113086 A113087 A113088

Keyword

nonn

Author

Paul D. Hanna, Oct 14 2005

Status

approved