1,2

Sum of n-th row terms = F(2n). Example: sum of 4-th row terms = ( 8 + 7 + 5 + 1) = 21 = F(8).

In companion triangle A140068, row sums = odd 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, with rest zeros. Perform X * [1,0,0,0,...], X * result, etc; with the result of each operation generating successive rows of the triangle.

First few rows of the triangle are:

1;

2, 1;

4, 3, 1;

8, 7, 5, 1;

16, 15, 17, 6, 1;

32, 31, 49, 23, 8, 1;

64, 63, 129, 72, 39, 9, 1;

128, 127, 321, 201, 150, 48, 11, 1;

256, 255, 769, 522, 501, 198, 70, 12, 1;

512, 511, 1793, 1291, 1524, 699, 338, 82, 14, 1;

1024, 1023, 4097, 3084, 4339, 2223, 1375, 420, 110, 15, 1;

...

Cf. A140068.

Sequence in context: A048483 A055248 A103316 this_sequence A105851 A106195 A051129

Adjacent sequences: A140066 A140067 A140068 this_sequence A140070 A140071 A140072

nonn,tabl

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