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
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Dec 01 2007
STATUS
approved