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Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,0,0,0,...] where X = an infinite lower triangular matrix with [1,2,1,2,1,2,...] in the main diagonal and [1,1,1,...] in the subdiagonal.
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%I #9 Dec 11 2019 09:48:36

%S 1,1,1,1,3,1,1,7,4,1,1,15,11,6,1,1,31,26,23,7,1,1,63,57,72,30,9,1,1,

%T 127,120,201,102,48,10,1,1,255,247,522,303,198,58,12,1,1,511,502,1291,

%U 825,699,256,82,13,1,1,1023,1013,3084,2116,2223,955,420,95,15,1,1,2047,2036

%N Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,0,0,0,...] where X = an infinite lower triangular matrix with [1,2,1,2,1,2,...] in the main diagonal and [1,1,1,...] in the subdiagonal.

%C Sum of n-th row terms = odd-indexed Fibonacci numbers, F(2n+1); e.g. sum of row 5 terms = (1 + 15 + 11 + 6 + 1) = 34 = F(9).

%C The triangle is a companion to A140069 (having row sums = even-indexed Fibonacci numbers).

%F Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,0,0,0,...] where X = an infinite lower triangular matrix with [1,2,1,2,1,2,...] in the main diagonal and [1,1,1,...] in the subdiagonal. Given the matrix X, perform X * [1,0,0,0,...] and then iterate: X * (result), etc. and record the result as each successive row of the triangle.

%e First few rows of the triangle are:

%e 1;

%e 1, 1;

%e 1, 3, 1;

%e 1, 7, 4, 1;

%e 1, 15, 11, 6, 1;

%e 1, 31, 26, 23, 7, 1;

%e 1, 63, 57, 72, 30, 9, 1;

%e 1, 127, 120, 201, 102, 48, 10, 1;

%e 1, 255, 247, 522, 303, 198, 58, 12, 1;

%e ...

%Y Cf. A140069.

%K nonn,tabl

%O 1,5

%A _Gary W. Adamson_ and _Roger L. Bagula_, May 04 2008