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 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]. 6
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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 * A220115 A039924 A275346 Adjacent sequences:  A093651 A093652 A093653 * A093655 A093656 A093657 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Apr 08 2004 STATUS approved

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Last modified May 14 16:00 EDT 2021. Contains 343884 sequences. (Running on oeis4.)