A136521 Triangle read by rows: (1, 2, 2, 2, ...) on the main diagonal and the rest zeros.

1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2

Offset: 0

Author

Gary W. Adamson, Jan 02 2008

Keywords

• nonn
• tabl
• less
• easy

Examples

			First few rows of the triangle are:
  1;
  0, 2;
  0, 0, 2;
  0, 0, 0, 2;
  0, 0, 0, 0, 2;
  ...
		

Links

• G. C. Greubel, Rows n = 0..25 of the triangle, flattened

Crossrefs

Cf. A001263, A007318, A040000, A124927, A134058, A136522.

Programs

Mathematica

Table[2*Boole[k==n] -Boole[n==0], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, May 03 2021 *)

Sage

flatten([[2*bool(k==n) -bool(n==0) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 03 2021

Formula

By columns, (1, 0, 0, 0, ...) in leftmost column; all others are (2, 0, 0, 0, ...).

By rows, row 1 = 1, others = (n-1) zeros followed by "2".

A007318(n,k) * T(n,k) = A124927(n,k).

T(n,k) * A007318(n,k) = A134058(n,k).

A001263(n,k) * T(n,k) = A136522(n,k).

From G. C. Greubel, May 03 2021: (Start)

T(n, k) = 2*[k=n] - [n=0].

Sum_{k=0..n} T(n, k) = A040000(n). (End)

Extensions

More terms added by G. C. Greubel, May 03 2021