A093654 - OEIS

%I #4 Mar 30 2012 18:36:40

%S 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 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 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 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 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 First column: T(2^n, 1) = A008934(n) for n>=0.

%e Let M(n) be the lower triangular matrix formed from the first 2^n rows.

%e To generate M(3) from M(2), take the matrix square of M(2):

%e [1,0,0,0]^2=[1,0,0,0]

%e [1,1,0,0]...[2,1,0,0]

%e [1,0,1,0]...[2,0,1,0]

%e [2,1,2,1]...[7,2,4,1]

%e and append M(2)^2 to the bottom left and bottom right of M(2):

%e [1],

%e [1,1],

%e [1,0,1],

%e [2,1,2,1],

%e .........

%e [1,0,0,0],[1],

%e [2,1,0,0],[2,1],

%e [2,0,1,0],[2,0,1],

%e [7,2,4,1],[7,2,4,1].

%e Repeating this process converges to triangle A093654.

%Y Cf. A008934, A093655, A093656, A093657, A093658.

%K nonn,tabl

%O 1,7

%A _Paul D. Hanna_, Apr 08 2004