A155031 Triangle T(n, k) = 0 if n==0 (mod k) otherwise -1 with T(n, n) = 1 and T(n, 0) = 0, read by rows.

1, 0, 1, 0, -1, 1, 0, 0, -1, 1, 0, -1, -1, -1, 1, 0, 0, 0, -1, -1, 1, 0, -1, -1, -1, -1, -1, 1, 0, 0, -1, 0, -1, -1, -1, 1, 0, -1, 0, -1, -1, -1, -1, -1, 1, 0, 0, -1, -1, 0, -1, -1, -1, -1, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1, -1, -1, -1, -1, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1

Offset

1,1

Links

G. C. Greubel, Rows n = 1..30 of the triangle, flattened

Formula

T(n, k) = A154990(n, k) * A155029(n, k).

T(n, k) = 0 if n==0 (mod k) otherwise -1 with T(n, n) = 1 and T(n, 0) = 0.

Example

Table begins:
  1;
  0,  1;
  0, -1,  1;
  0,  0, -1,  1;
  0, -1, -1, -1,  1;
  0,  0,  0, -1, -1,  1;
  0, -1, -1, -1, -1, -1,  1;
  0,  0, -1,  0, -1, -1, -1,  1;
  0, -1,  0, -1, -1, -1, -1, -1, 1;

Mathematica

T[n_, k_]:= If[k==n, 1, If[k==1 || Mod[n, k]==0, 0, -1]];
Table[T[n, k], {n, 12}, {k, n}] //Flatten (* G. C. Greubel, Mar 08 2021 *)

Prog

(Sage) flatten([[1 if k==n else 0 if (k==1 or n%k==0) else -1 for k in [1..n]] for n in [1..12]]) # G. C. Greubel, Mar 08 2021
(Magma) [k eq n select 1 else (k eq 1 or n mod k eq 0) select 0 else -1: k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 08 2021

Crossrefs

Cf. A154990, A155029.

Sequence in context: A187034 A101688 A155029 * A134540 A318962 A128430

Adjacent sequences: A155028 A155029 A155030 * A155032 A155033 A155034

Keyword

sign,tabl

Author

Mats Granvik, Jan 19 2009

Status

approved