cp's OEIS Frontend

A093654 Lower triangular matrix, read by rows, defined as the convergent of the concatenation of matrices using the iteration: M(n+1) = [[M(n),0*M(n)],[M(n)^2,M(n)^2]], with M(0) = [1].

%I A093654 #4 Mar 30 2012 18:36:40
%S A093654 1,1,1,1,0,1,2,1,2,1,1,0,0,0,1,2,1,0,0,2,1,2,0,1,0,2,0,1,7,2,4,1,7,2,
%T A093654 4,1,1,0,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,2,1,2,0,1,0,0,0,0,0,2,0,1,7,2,
%U A093654 4,1,0,0,0,0,7,2,4,1,2,0,0,0,1,0,0,0,2,0,0,0,1,7,2,0,0,4,1,0,0,7,2,0,0,4,1
%N A093654 Lower triangular matrix, read by rows, defined as the convergent of the concatenation of matrices using the iteration: M(n+1) = [[M(n),0*M(n)],[M(n)^2,M(n)^2]], with M(0) = [1].
%C A093654 Related to the number of tournament sequences (A008934). First column forms A093655, where A093655(2^n) = A008934(n) for n>=0. Row sums form A093656, where A093656(2^(n-1)) = A093657(n) for n>=1.
%F A093654 First column: T(2^n, 1) = A008934(n) for n>=0.
%e A093654 Let M(n) be the lower triangular matrix formed from the first 2^n rows.
%e A093654 To generate M(3) from M(2), take the matrix square of M(2):
%e A093654 [1,0,0,0]^2=[1,0,0,0]
%e A093654 [1,1,0,0]...[2,1,0,0]
%e A093654 [1,0,1,0]...[2,0,1,0]
%e A093654 [2,1,2,1]...[7,2,4,1]
%e A093654 and append M(2)^2 to the bottom left and bottom right of M(2):
%e A093654 [1],
%e A093654 [1,1],
%e A093654 [1,0,1],
%e A093654 [2,1,2,1],
%e A093654 .........
%e A093654 [1,0,0,0],[1],
%e A093654 [2,1,0,0],[2,1],
%e A093654 [2,0,1,0],[2,0,1],
%e A093654 [7,2,4,1],[7,2,4,1].
%e A093654 Repeating this process converges to triangle A093654.
%Y A093654 Cf. A008934, A093655, A093656, A093657, A093658.
%K A093654 nonn,tabl
%O A093654 1,7
%A A093654 _Paul D. Hanna_, Apr 08 2004