A127445 Triangle defined by the matrix product A126988 * A127368, read by rows.

1, 3, 0, 4, 2, 0, 7, 0, 3, 0, 6, 2, 3, 4, 0, 12, 4, 0, 0, 5, 0, 8, 2, 3, 4, 5, 6, 0, 15, 0, 9, 0, 5, 0, 7, 0, 13, 8, 0, 4, 5, 0, 7, 8, 0, 18, 4, 9, 8, 0, 0, 7, 0, 9, 0, 12, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 28, 8, 9, 0, 15, 0, 7, 0, 0, 0, 11

Offset: 1

Author

Gary W. Adamson, Jan 14 2007

Keywords

• nonn
• tabl

Examples

			First few rows of the triangle are:
1;
3, 0;
4, 2, 0;
7, 0, 3, 0;
6, 2, 3, 4, 0;
12, 4, 0, 0, 5, 0;
8, 2, 3, 4, 5, 6, 0;
...
		

Crossrefs

Cf. A126988, A127368, A000217 (row sums), A000203 (column k=1).

Programs

Maple

A127368:=proc(n, k) if igcd(n,k) = 1 then k else 0 fi end:
A127445 := proc(n,k)
        add (A126988(n,j)*A127368(j,k),j=k..n) ;
end proc:
seq(seq(A127445(n,k),k=1..n),n=1..14) ; # R. J. Mathar, Nov 11 2011

Formula

T(n,k) = Sum_{j=k..n} A126988(n,j) * A127368(j,k), 1<=k<=n.