1,3

Row sums = A133914: (1, 3, 5, 11, 23, 44, 89, 177, 355,...). Right border = A007001: (1, 2, 1, 2, 3, 1, 2, 1,...).

Given A007001: (1, 2, 1, 2, 3, 1, 2, 1,...) as first row of an array, n-th row = partial sum sequence of (n-1)-th row. The Triangle A133913 = the antidiagonals of this array.

First few rows of the array are:

1, 2, 1, 2, 3, 1, 2,...

1, 3, 4, 6, 9, 10, 12,...

1, 4, 8, 14, 23, 33, 45,...

1, 5, 13, 27, 50, 83, 128,...

1, 6, 19, 46, 96, 179, 307,...

...

First few rows of the triangle are:

1;

1, 2;

1, 3, 1;

1, 4, 4, 2;

1, 5, 8, 6, 3;

1, 6, 13, 14, 9, 1;

1, 7, 19, 27, 23, 10, 2;

1, 8, 26, 46, 50, 33, 12, 1;

1, 9, 34, 72, 96, 83, 45, 13, 2;

1, 10, 43, 106, 168, 179, 128, 58, 15, 3;

...

Cf. A007001, A133912, A133914.

Sequence in context: A124033 A112543 A099478 this_sequence A141412 A026807 A106740

Adjacent sequences: A133910 A133911 A133912 this_sequence A133914 A133915 A133916

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 28 2007