1,5

First few rows of the array are:

Create an array by rows: (binomial transforms of 1,0,0,0,...; 1,2,0,0,0...; 1,2,3,0,0,0...; etc). Antidiagonals of the array become rows of the triangle.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...

1, 3, 5, 7, 9, 11, 13, 15, 17,...

1, 3, 8, 16, 27, 41, 58, 78, 101,...

1, 3, 8, 20, 43, 81, 138, 218,...

1, 3, 8, 20, 48, 106, 213,...

1, 3, 8, 20, 48, 112, 249,...

...

Rows converge to A001792, binomial transform of (1,2,3...); and the first few rows of the triangle are:

1

1, 1;

1, 3, 1;

1, 3, 5, 1;

1, 3, 8, 7, 1;

1, 3, 8, 16, 9, 1;

1, 3, 8, 20, 27, 22, 1;

...

Row sums are Fibonacci numbers convolved with themselves (A001629: 1, 2, 5, 10, 20, 38, 71, 130, 235, 420...).

a(4), a(5), a(6) = 1, 3, 1 = antidiagonals of the array becoming row three of the triangle.

Cf. A001629, A104249.

Sequence in context: A097560 A027960 A131248 this_sequence A110291 A077308 A075001

Adjacent sequences: A116442 A116443 A116444 this_sequence A116446 A116447 A116448

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 15 2006