A093654 - OEIS

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].

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, 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, 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

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OFFSET

1,7

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..105.

FORMULA

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

EXAMPLE

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

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

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

[1,1,0,0]...[2,1,0,0]

[1,0,1,0]...[2,0,1,0]

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

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