A134402 Triangle read by rows, for n > 0, n zeros followed by n.

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

Offset: 0

Author

Gary W. Adamson, Oct 23 2007

Keywords

• nonn
• easy
• tabl

Comments

Multiplied by the vector [1, 2, 3, ...] from the right gives (1, 2, 6, 12, 20, 30, 42, ...), A002378.

Triangle T(n,k), read by rows, given by [0,0,0,0,0,0,0,...] DELTA [1,1,-1,1,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 26 2007

Examples

			First few rows of the triangle:
  1;
  0, 1;
  0, 0, 2;
  0, 0, 0, 3;
  0, 0, 0, 0, 4;
  0, 0, 0, 0, 0, 5;
  ...
		

Crossrefs

Cf. A134403, A005449.

Essentially the same as A130460.

Programs

Mathematica

Join[{1},Flatten[Table[PadLeft[{n},n+1,0],{n,15}]]] (* Harvey P. Dale, May 08 2012 *)

Formula

Triangle read by rows, a(0) = 1, then for n > 0, n zeros followed by n. Infinite lower triangular matrix with (1, 1, 2, 3, 4, ...) in the main diagonal and the rest zeros.

G.f.: (1-x*y+x^2*y^2)/(-1+x*y)^2. - R. J. Mathar, Aug 11 2015