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.
%I A113078 #11 Dec 12 2021 22:54:00
%S A113078 1,4,26,274,4721,134899,6501536,537766009,77598500096,19821981700354,
%T A113078 9077118324755246,7531446638893873684,11423775838657143826346,
%U A113078 31914367054676982206368909,165251261153335414813452988541
%N 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.
%C A113078 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.
%H A113078 M. Cook and M. Kleber, <a href="https://doi.org/10.37236/1522">Tournament sequences and Meeussen sequences</a>, Electronic J. Comb. 7 (2000), #R44.
%e A113078 The tree of tournament sequences of descendents of a node labeled (4) begins:
%e A113078 [4]; generation 1: 4->[5,6,7,8]; generation 2: 5->[6,7,8,9,10],
%e A113078 6->[7,8,9,10,11,12], 7->[8,9,10,11,12,13,14],
%e A113078 8->[9,10,11,12,13,14,15,16]; ...
%e A113078 Then a(n) gives the number of nodes in generation n.
%e A113078 Also, a(n+1) = sum of labels of nodes in generation n.
%o A113078 (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])}
%Y A113078 Cf. A113077, A113079, A008934, A113089, A113096, A113098, A113100, A113107, A113109, A113111, A113113.
%K A113078 nonn
%O A113078 0,2
%A A113078 _Paul D. Hanna_, Oct 14 2005