A062534 -id:A062534 - cp's OEIS frontend

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

Benoit Cloitre, Feb 28 2004

Row sums give A038573.

			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; ...

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

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

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 *)

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

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

cp's OEIS Frontend

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

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