A143214 Gray code applied to Pascal's triangle: T(n,k) = GrayCode(binomial(n, k)).

1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 6, 5, 6, 1, 1, 7, 15, 15, 7, 1, 1, 5, 8, 30, 8, 5, 1, 1, 4, 31, 50, 50, 31, 4, 1, 1, 12, 18, 36, 101, 36, 18, 12, 1, 1, 13, 54, 126, 65, 65, 126, 54, 13, 1, 1, 15, 59, 68, 187, 130, 187, 68, 59, 15, 1

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Oct 20 2008

Keywords

• nonn
• tabl

Examples

			Triangle begins as:
  1;
  1,  1;
  1,  3,  1;
  1,  2,  2,   1;
  1,  6,  5,   6,   1;
  1,  7, 15,  15,   7,   1;
  1,  5,  8,  30,   8,   5,   1;
  1,  4, 31,  50,  50,  31,   4,  1;
  1, 12, 18,  36, 101,  36,  18, 12,  1;
  1, 13, 54, 126,  65,  65, 126, 54, 13,  1;
  1, 15, 59,  68, 187, 130, 187, 68, 59, 15, 1;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened
• Eric Weisstein, Mathematica Notebook GrayCode.nb
• Eric Weisstein, Gray Code, MathWorld.

Crossrefs

Cf. A143213.

Programs

Mathematica

GrayCode[n_, k_]:= FromDigits[BitXor@@@Partition[Prepend[IntegerDigits[n, 2, k], 0], 2, 1], 2];
A143214[n_, k_]:= GrayCode[Binomial[n-1, k-1], 10];
Table[A143214[n,k], {n,12}, {k,n}]//Flatten

Extensions

Edited by Michel Marcus and Joerg Arndt, Apr 22 2013

Edited by G. C. Greubel, Aug 27 2024