1,3

Terms in the array rows tend to A001787, number of edges in n-dimensional hypercubes: 1, 4, 12, 32, 80, 192, 448... Row sums of the sequence also = A001787.

From an array, rows = binomial transforms of (1,0,0,0...); (1,3,0,0,0...); (1,3,5,0,0,0...); difference rows of the columns become rows of the triangle.

First few rows of the array are:

1 1 1 1 1...

1 4 7 10 13...

1 4 12 25 43...

1 4 12 32 71...

1 4 12 32 80...

...

Then take differences of columns which become rows of the triangle:

1;

1, 3;

1, 6, 5;

1, 9, 15, 7;

1, 12, 30, 28, 9;

1, 15, 50, 70, 45, 11;

1, 18, 75, 140, 135, 66, 13;

1, 21, 105, 245, 315, 231, 91, 15;

...

Cf. A001787.

Adjacent sequences: A116663 A116664 A116665 this_sequence A116667 A116668 A116669

Sequence in context: A007383 A120394 A016575 this_sequence A061702 A112351 A143858

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 22 2006