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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]. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,9

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.

LINKS

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

EXAMPLE

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.

Sequence in context: A286564 A316359 A080080 * A284256 A250211 A243753

Adjacent sequences:  A093659 A093660 A093661 * A093663 A093664 A093665

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Apr 08 2004

STATUS

approved

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Last modified July 21 18:06 EDT 2019. Contains 325198 sequences. (Running on oeis4.)