A140820 Triangle read by rows: T(n,k) = 1 if and only if the Gray codes for n and k have no bits in common.

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

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Oct 17 2008

Keywords

• nonn
• tabl
• less
• changed

Examples

			Triangle begins as:
  1;
  1, 0;
  1, 0, 0;
  1, 1, 0, 0;
  1, 1, 0, 0, 0;
  1, 0, 0, 0, 0, 0;
  1, 0, 0, 1, 0, 0, 0;
  1, 1, 1, 1, 0, 0, 0, 0;
  1, 1, 1, 1, 0, 0, 0, 0, 0;
  1, 0, 0, 1, 0, 0, 0, 0, 0, 0;
  1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
  1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
		

Links

• G. C. Greubel, Rows n = 0..100 of the triangle, flattened

Crossrefs

Cf. A131218.

Programs

Magma

A140280:= func< n,k | BitwiseAnd(BitwiseXor(n, ShiftRight(n, 1)), BitwiseXor(k, ShiftRight(k, 1))) eq 0 select 1 else 0 >; // based on Kevin Ryde's code
[A140280(n, k): k in [0..n], n in [0..15]]; // G. C. Greubel, Sep 05 2025

Mathematica

A140820[n_, k_]:= Boole[BitAnd[BitXor[n,BitShiftRight[n,1]], BitXor[k,BitShiftRight[k, 1]]]==0]; (* based on Kevin Ryde's code *)
Table[A140280[n,k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, May 30 2019; Sep 05 2025 *)

PARI

T(n,k) = !bitand(bitxor(n,n>>1), bitxor(k,k>>1)); \\ Kevin Ryde, Jul 13 2020

SageMath

def A140820(n,k): return int( (n^^(n>>1)) & (k^^(k>>1)) ==0) # based on Kevin Ryde's code
print(flatten([[A140820(n, k) for k in range(n+1)] for n in range(16)])) # G. C. Greubel, May 30 2019; Sep 05 2025

Extensions

Edited by G. C. Greubel, May 30 2019

New title from Charlie Neder, Jun 03 2019

Offset changed by G. C. Greubel, Sep 05 2025