1,5

Row terms sums of the triangle = the Pell sequence A000129: (1, 2, 5, 12, 29...). Right border of the triangle = inverse binomial transform of the Pell sequence: (A016116): (1, 1, 2, 2, 4, 4,...).

The triangle = difference terms of columns from an array generated from binomial transforms of (1,0,0,0...); (1,1,0,0,0...); (1,1,2,2...); (1,1,2,2,4,...); where (1, 1, 2, 2, 4, 4,...) = A016116, the inverse binomial transform of the Pell sequence A000129..

Triangle read by rows, iterates of X * [1,0,0,0,...] where X = an infinite bidiagonal matrix with (1,1,1,...) in the main diagonal and (1,2,1,2,1,2,...) in the subdiagonal, with the rest zeros. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 10 2008

First few rows of the generating array are:

1, 1, 1, 1, 1,...

1, 2, 3, 4, 5,...

1, 2, 5, 10, 17,...

1, 2, 5, 12, 25,...

1, 2, 5, 12, 29,...

...

Taking difference terms of the columns, we get the triangle A117919. First few rows are:

1;

1, 1;

1, 2, 2;

1, 3, 6, 2;

1, 4, 12, 8, 4;

1, 5, 20, 20, 20, 4;

1, 6, 30, 40, 60, 24, 8;

1, 7, 42, 70, 140, 84, 56, 8;

...

Cf. A000129, A016116.

Sequence in context: A071944 A080955 A125231 this_sequence A068956 A124842 A134399

Adjacent sequences: A117916 A117917 A117918 this_sequence A117920 A117921 A117922

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 02 2006