A113096 Number of 4-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 3) and t_{i+1} <= 4*t_i for 1<i<n.

1, 1, 4, 46, 1504, 146821, 45236404, 46002427696, 159443238441379, 1926751765436372746, 82540801108546193896804, 12696517688186899788062326096, 7084402815778394692932546017050054

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..12.

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

Example

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.

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

Crossrefs

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

Sequence in context: A210855 A324228 A002077 * A135078 A195243 A269005

Adjacent sequences: A113093 A113094 A113095 * A113097 A113098 A113099

Keyword

nonn

Author

Paul D. Hanna, Oct 14 2005

Status

approved