1,5

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).

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

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.

First few rows of the triangle are:

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

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

...

Cf. A140069.

Sequence in context: A135288 A078026 A126713 this_sequence A121300 A128119 A112996

Adjacent sequences: A140065 A140066 A140067 this_sequence A140069 A140070 A140071

nonn,tabl

Gary W. Adamson and Roger L. Bagula (qntmpkt(AT)yahoo.com), May 04 2008