0,6

Right border = Motzkin numbers, A001006: (1, 1, 2, 4, 9, 21,...).

Row sums = (1, 2, 4, 9, 21,...);

Left border = A086246: (1, 1, 1, 2, 4, 9, 21,...).Q Sum of n-th row terms = rightmost term of next row.

Let A = an infinite lower triangular matrix with A086246: (1, 1, 1, 2, 4, 9, 21, 51,...) in every column; and B = an infinite lower triangular matrix with A001006, (1, 1, 2, 4, 9, 21,...) as the main diagonal and the rest zeros.

a144218 = A*B.

First few rows of the triangle =

1;

1, 1;

1, 1, 2;

2, 1, 2, 4;

4, 2, 2, 4, 9;

9, 4, 4, 4, 9, 21;

21, 9, 8, 8, 9, 21, 51;

51, 21, 18, 16, 18, 21, 51, 127;

127, 51, 42, 36, 36, 42, 51, 127, 323;

323, 127, 102, 84, 81, 84, 102, 127, 323, 835;

835, 323, 254, 204, 189, 189, 204, 254, 835, 2188;

...

Row 4 = (4, 2, 2, 4, 9) = termwise products of (4, 2, 1, 1, 1) and (1, 1, 2, 4, 9) = (4*1, 2*1, 1*2, 1*4, 1*9).

A001006, Cf. A086246

Sequence in context: A144963 A035374 A048299 this_sequence A098691 A035364 A143808

Adjacent sequences: A144215 A144216 A144217 this_sequence A144219 A144220 A144221

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 14 2008