A134394 Triangle T(n,k) = Sum_{j=k..n} A077028(j,k), read by rows.

1, 2, 1, 3, 3, 1, 4, 6, 4, 1, 5, 10, 9, 5, 1, 6, 15, 16, 12, 6, 1, 7, 21, 25, 22, 15, 7, 1, 8, 28, 36, 35, 28, 18, 8, 1, 9, 36, 49, 51, 45, 34, 21, 9, 1, 10, 45, 64, 70, 66, 55, 40, 24, 10, 1, 11, 55, 81, 92, 91, 81, 65, 46, 27, 11, 1, 12, 66, 100, 117, 120, 112, 96, 75, 52, 30, 12, 1, 13, 78, 121, 145, 153

Offset: 1

Author

Gary W. Adamson, Oct 23 2007

Keywords

• nonn
• tabl

Comments

Row sums = A055795: (1, 3, 7, 15, 30, 56, 98, ...).

Antidiagonal reading of A139600 without its left column. - R. J. Mathar, Apr 17 2011

Examples

			First few rows of the triangle:
  1;
  2,  1;
  3,  3,  1;
  4,  6,  4,  1;
  5, 10,  9,  5,  1;
  6, 15, 16, 12,  6,  1;
  7, 21, 25, 22, 15,  7,  1;
		

Crossrefs

Cf. A077028, A055795, A139600.

Programs

Maple

A077028 := proc(n,k) if n < 0 or k<0 or k > n then 0; else k*(n-k)+1 ; end if; end proc:
A134394 := proc(n,k) add ( A077028(j,k),j=k..n) ; end proc:
seq(seq(A134394(n,k),k=0..n),n=0..15) ; # R. J. Mathar, Apr 17 2011

Formula

A000012 * A077028 as infinite lower triangular matrices.

T(n,k) = (k-n-1)*(k*(k-n)-2)/2. - R. J. Mathar, Apr 17 2011