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

1,2

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

Links

Table of n, a(n) for n=1..83.

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

Example

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;

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

Crossrefs

Cf. A077028, A055795, A139600.

Sequence in context: A373169 A225281 A057145 * A322967 A284855 A074909

Adjacent sequences: A134391 A134392 A134393 * A134395 A134396 A134397

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 23 2007

Status

approved