cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A113079 Number of tournament sequences: a(n) gives the number of n-th generation descendents of a node labeled (5) in the tree of tournament sequences.

Original entry on oeis.org

1, 5, 40, 515, 10810, 376175, 22099885, 2231417165, 393643922005, 123097221805100, 69087264010363930, 70321483026073531730, 130954011392485408662370, 449450774746306949114288795
Offset: 0

Views

Author

Paul D. Hanna, Oct 14 2005

Keywords

Comments

Equals column 5 of square table A093729. Also equals column 0 of the matrix 5th power 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.

Examples

			The tree of tournament sequences of descendents of a node labeled (5) begins:
[5]; generation 1: 5->[6,7,8,9,10]; generation 2:
6->[7,8,9,10,11,12], 7->[8,9,10,11,12,13,14],
8->[9,10,11,12,13,14,15,16], 9->[10,11,12,13,14,15,16,17,18],
10->[11,12,13,14,15,16,17,18,19,20]; ...
Then a(n) gives the number of nodes in generation n.
Also, a(n+1) = sum of labels of nodes in generation n.
		

Crossrefs

Programs

  • 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^5)[n+1,1])}