A113128 A simple 4-diagonal matrix based on (1+x)^3.

1, 3, 2, 3, 6, 3, 1, 6, 9, 4, 0, 2, 9, 12, 5, 0, 0, 3, 12, 15, 6, 0, 0, 0, 4, 15, 18, 7, 0, 0, 0, 0, 5, 18, 21, 8, 0, 0, 0, 0, 0, 6, 21, 24, 9, 0, 0, 0, 0, 0, 0, 7, 24, 27, 10, 0, 0, 0, 0, 0, 0, 0, 8, 27, 30, 11, 0, 0, 0, 0, 0, 0, 0, 0, 9, 30, 33, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 33, 36, 13, 0, 0, 0, 0

Offset

0,2

Comments

Row sums are A086570. Diagonal sums are the odd numbers A005408.

Links

Table of n, a(n) for n=0..94.

Formula

Number triangle where column k has g.f. (1+x)^3*(k+1)x^k.

Example

Triangle begins
1;
3, 2;
3, 6, 3;
1, 6, 9, 4;
0, 2, 9, 12, 5;
0, 0, 3, 12, 15, 6;
0, 0, 0, 4, 15, 18, 7;
0, 0, 0, 0, 5, 18, 21, 8;

Crossrefs

Sequence in context: A343368 A021313 A240162 * A220075 A266593 A130459

Adjacent sequences: A113125 A113126 A113127 * A113129 A113130 A113131

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 14 2005

Status

approved