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

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):
[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].
Repeating this process converges to triangle A093654.

Crossrefs

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

Sequence in context: A158566 A128410 A059782 * A342627 A220115 A039924

Adjacent sequences: A093651 A093652 A093653 * A093655 A093656 A093657

Keyword

nonn,tabl

Author

Paul D. Hanna, Apr 08 2004

Status

approved