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

0,3

Links

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

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)

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A340988 A134013 A112301 * A066448 A108497 A108498

Adjacent sequences: A136518 A136519 A136520 * A136522 A136523 A136524

Keyword

nonn,tabl,less,easy

Author

Gary W. Adamson, Jan 02 2008

Extensions

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

Status

approved