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

0,1

Links

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

Example

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;

Mathematica

A140820[n_, k_]:= Boole[BitAnd[BitXor[n, BitShiftRight[n, 1]], BitXor[k, BitShiftRight[k, 1]]]==0]; (* based on Kevin Ryde's code *)
Table[A140820[n, k], {n, 0, 13}, {k, 0, n}]//Flatten (* G. C. Greubel, May 30 2019; Sep 05 2025 *)

Prog

(PARI) T(n, k) = !bitand(bitxor(n, n>>1), bitxor(k, k>>1)); \\ Kevin Ryde, Jul 13 2020
(Magma)
A140820:= 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
[A140820(n, k): k in [0..n], n in [0..15]]; // G. C. Greubel, Sep 05 2025
(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

Crossrefs

Cf. A131218.

Sequence in context: A176918 A176890 A164057 * A275661 A266716 A190242

Adjacent sequences: A140817 A140818 A140819 * A140821 A140822 A140823

Keyword

nonn,tabl,less

Author

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

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

Status

approved