A083651 Triangular array, read by rows: T(n,k) = k-th bit in binary representation of n (0<=k<=n).

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

Offset: 0

Author

Reinhard Zumkeller, May 01 2003

Keywords

• nonn
• tabl
• easy

Comments

n = Sum(T(n,k)*2^k: 0<=k<=n);

T(n, A070939(n))=1 for n>0, T(n,k)=0 for k>A070939(n);

T(n,0)=A000035(n); T(n,n)=0;

A021913(0)=T(0,0), A021913(n)=T(n,1) for n>0.

Examples

			The triangle starts
0
1 0
0 1 0
1 1 0 0
0 0 1 0 0
1 0 1 0 0 0
0 1 1 0 0 0 0
1 1 1 0 0 0 0 0
0 0 0 1 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0
0 1 0 1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0 0 0 0 0 0
		

Crossrefs

Cf. A000035 (column k=0), A133872 (k=1), A131078 (k=2), A000120 (row sums).

Programs

Maple

A083651 := proc(n,k)
    floor(n/2^k) ;
    modp(%,2) ;
end proc:  # R. J. Mathar, Apr 21 2021

Mathematica

row[n_] := row[n] = PadRight[Reverse[IntegerDigits[n, 2]], n+1];
T[n_, k_] := row[n][[k+1]];
Table[T[n, k], {n, 0, 14}, {k, 0, n}] // Flatten