1,3

Row sums = A053220: (1, 5, 16, 44, 112...), binomial transform of (A016777): (1, 4, 7,...)

Given (3n + 1): 1, 4, 7...; take binomial transforms of (1,0,0,0...); (1,4,0,0,0...); (1,4,7,0,0.0...) forming an array. Difference terms of the array columns become row of the triangle.

First few rows of the array are:

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

1, 5, 9, 13, 17,...

1, 5, 16, 34, 59,...

1, 5, 16, 44, 99,...

...

First few rows of the triangle are:

1;

1, 4;

1, 8, 7;

1, 12, 21, 10;

1, 16, 42, 40, 13;

1, 24, 66, 100, 65, 16;

1, 28, 101, 200, 195, 96, 19;

...

Cf. A016777, A053220.

Sequence in context: A143820 A103553 A067439 this_sequence A128414 A019699 A125092

Adjacent sequences: A116921 A116922 A116923 this_sequence A116925 A116926 A116927

nonn,tabl,uned

Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 26 2006