A101309 Matrix logarithm of A047999 (Pascal's triangle mod 2).

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

Offset: 0

Author

Paul D. Hanna, Dec 23 2004

Keywords

• nonn
• tabl

Comments

Row sums equal A000120 (binary 1's-counting sequence). Antidiagonal sums form A101979.

Examples

			T(n,k)=1 when n XOR k is a power of 2:
T(3,2)=1 since 3 XOR 2 = 2^0, T(4,0)=1 since 4 XOR 0 = 2^2,
T(5,1)=1 since 5 XOR 1 = 2^2, T(6,4)=1 since 6 XOR 4 = 2^2.
Rows begin:
[0],
[1, 0],
[1,0, 0],
[0,1, 1,0],
[1,0,0,0, 0],
[0,1,0,0, 1,0],
[0,0,1,0, 1,0,0],
[0,0,0,1, 0,1,1,0],...
		

Crossrefs

Cf. A047999, A101979.

Programs

PARI

T(n,k)=if(n>k&bitxor(n,k)==2^valuation(bitxor(n,k),2),1,0)

Formula

T(n, k)=1 when n XOR k = 2^m for integer m>=0, T(n, k)=0 elsewhere.