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.

A113078 Number of tournament sequences: a(n) gives the number of n-th generation descendents of a node labeled (4) in the tree of tournament sequences.

Original entry on oeis.org

1, 4, 26, 274, 4721, 134899, 6501536, 537766009, 77598500096, 19821981700354, 9077118324755246, 7531446638893873684, 11423775838657143826346, 31914367054676982206368909, 165251261153335414813452988541
Offset: 0

Views

Author

Paul D. Hanna, Oct 14 2005

Keywords

Comments

Equals column 4 of square table A093729. Also equals column 0 of the matrix 4th 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 (4) begins:
[4]; generation 1: 4->[5,6,7,8]; generation 2: 5->[6,7,8,9,10],
6->[7,8,9,10,11,12], 7->[8,9,10,11,12,13,14],
8->[9,10,11,12,13,14,15,16]; ...
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^4)[n+1,1])}