A135839 Triangle read by rows: starting with A138174, 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

1,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows

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

Example

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;
...

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 *)

Crossrefs

Sequence in context: A103994 A051731 A304569 * A071022 A155076 A328308

Adjacent sequences: A135836 A135837 A135838 * A135840 A135841 A135842

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 01 2007

Status

approved