A135839 Triangle read by rows: starting with A128174, replace left border with (1, 1, 1, ...).

1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1

Offset: 1

Author

Gary W. Adamson, Dec 01 2007

Keywords

• nonn
• tabl
• easy

Comments

Row sums = (1, 2, 2, 3, 3, 4, 4, 5, 5, ...).

Examples

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

Links

• Zhuorui He, Rows 1..150 of the triangle, flattened (first 50 rows from G. C. Greubel)

Programs

Mathematica

T[1, 1] := 1; T[n_, 1] := 1; T[n_, n_] := 1; T[n_, k_] := (1 - (-1)^(n - k + 1))/2; Table[T[n, k], {n, 1, 10}, {k, 1, n}]//Flatten (* G. C. Greubel, Dec 05 2016 *)
Flatten[Table[Join[{1},PadLeft[{},n,{0,1}]],{n,0,20}]] (* Harvey P. Dale, Feb 26 2024 *)

Formula

Given A128174, replace left border with (1, 1, 1, ...). Triangle read by rows, odd rows = n terms of (1, 0, 1, ...); even rows = n terms of (1, 1, 0, 1, 0, 1, ...). By columns, leftmost column = (1, 1, 1, ...); all others = (1, 0, 1, 0, 1, ...).

T(n,1) = T(n,n) = 1, T(n,k) = (1 - (-1)^(n-k-1))/2. - G. C. Greubel,Dec 05 2016

Extensions

Definition corrected by Zhuorui He, Jul 21 2025