0,3

Successive deletions of the right borders of triangle A117894 produces triangles whose row sums = generalized Pell sequences starting (1, 2...), (1, 3...), (1, 4...); etc. Row sums of A117894 = A000129: (1, 2, 5...). Row sums of A117895 = A001333: (1, 3, 7...). Deletion of the border of A117895 would produce a triangle with row sums of the Pell sequence A048654 (1, 4, 9...); and so on.

Delete right border of triangle A117894. Alternatively, let row 1 = 1, and using the heading 0, 1, 1, 3, 7, 17, 41, 99, 239...(i.e. A001333 starting with 0, 1, 1, 3...); add the first n terms of the heading to n-th row of triangle A117894.

First few rows of the triangle are:

1;

1, 2;

1, 3, 3;

1, 4, 4, 8;

1, 5, 5, 11, 19;

1, 6, 6, 14, 26, 46;

1, 7, 7, 17, 33, 63, 111;

1, 8, 8, 20, 40, 80, 152, 268;

...

Row 4, (1, 4, 4, 8) is produced by adding (0, 1, 1, 3) to row 4 of A117894: (1, 3, 3, 5).

Cf. A117894, A000129, A001333, A048654, A048655, A048693.

Adjacent sequences: A117892 A117893 A117894 this_sequence A117896 A117897 A117898

Sequence in context: A134625 A054531 A115131 this_sequence A128139 A104732 A132108

nonn

Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 30 2006