A093662 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),M(n)^2]], with M(0) = [1].

1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 2, 0, 1, 1, 1, 2, 1, 5, 2, 4, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 2, 1, 0, 0, 0, 0, 5, 2, 4, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 2, 1, 0, 0, 5, 2, 0, 0, 4, 1

Offset: 1

Author

Paul D. Hanna, Apr 08 2004

Keywords

• nonn
• tabl

Comments

Row sums form A093663, where A093663(2^n) = A016121(n) for n>=0. The 2^n-th row converges to A093664, where A093664(2^n+1) = A016121(n) for n>=0.

Examples

			Let M(n) be the lower triangular matrix formed from the first 2^n rows.
To generate M(3) from M(2), obtain 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]
[1,1,2,1]...[5,2,4,1],
then M(3) is formed by starting with M(2) and appending M(2) to the bottom left and M(2)^2 to the bottom right:
[1],
[1,1],
[1,0,1],
[1,1,2,1],
..........
[1,0,0,0],[1],
[1,1,0,0],[2,1],
[1,0,1,0],[2,0,1],
[1,1,2,1],[5,2,4,1].
Repeating this process converges to triangle A093662.
		

Crossrefs

Cf. A016121, A093655, A093658, A093663, A093664.