A090971 Sierpiński's triangle, read by rows, starting from 1: T(n,k) = (T(n-1,k) + T(n-1,k-1)) mod 2.

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

Offset

1,1

Comments

Row sums give A038573.

Links

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Formula

From Philippe Deléham, Feb 29 2004: (Start)

Triangle A047999(n, k) for n,k > 0; A047999: Pascal's triangle mod 2.

a(n) = A062534(n-1) mod 2.

T(n-1, k-1) = A074909(n, n-k) mod 2. (End)

T(n, k) = 1 if bitand(n, k) = k, and 0 otherwise. - Amiram Eldar, Aug 24 2024

Example

Triangle begins with:
  1;
  0, 1;
  1, 1, 1;
  0, 0, 0, 1;
  1, 0, 0, 1, 1;
  0, 1, 0, 1, 0, 1;
  1, 1, 1, 1, 1, 1, 1; ...

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[k==n, 1, Mod[T[n-1, k] + T[n-1, k-1], 2]]]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] (* G. C. Greubel, Feb 03 2019 *)
Table[Boole[BitAnd[n, k] == k], {n, 1, 14}, {k, 1, n}] // Flatten (* Amiram Eldar, Aug 24 2024 *)

Prog

(PARI) T(n, k)=if(k<0 || k>n, 0, if(n==0, 1, (T(n-1, k)+T(n-1, k-1))%2))

Crossrefs

Cf. A007318, A038573, A047999, A062534, A074909.

Sequence in context: A267814 A267272 A181656 * A105594 A091949 A039984

Adjacent sequences: A090968 A090969 A090970 * A090972 A090973 A090974

Keyword

nonn,tabl

Author

Benoit Cloitre, Feb 28 2004

Status

approved