1,4

Row sums = A137681: (1, 2, 4, 10, 23, 56, 132,...). A variation of the same sequence = column 2 of the triangle: (1, 0, 2, 4, 10, 23, 56, 132,...) = first difference row of column 1. Left border of the triangle = A137682.

Triangle read by rows generated by two rules; T(n,k) = T(n-1, k-1) - T(n-k, k-1). Leftmost term in each row = sum of all previous terms in the triangle.

First few rows of the triangle are:

1;

1, 1;

3, 0, 1;

7, 2, 0, 1;

17, 4, 1, 0, 1;

40, 10, 4, 1, 0, 1;

96, 23, 8, 3, 1, 0, 1;

228, 56, 19, 8, 3, 1, 0, 1;

544, 132, 46, 18, 7, 3, 1, 0, 1;

1296, 316, 109, 42, 18, 7, 3, 1, 0, 1;

3089, 752, 260, 101, 41, 17, 7, 3, 1, 0, 1;

...

Cf. A137681, A137682.

Sequence in context: A111924 A100485 A143397 this_sequence A011074 A020816 A099097

Adjacent sequences: A137677 A137678 A137679 this_sequence A137681 A137682 A137683

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 05 2008