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

1,5

Links

G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Eric Weisstein, Mathematica Notebook GrayCode.nb

Eric Weisstein, Gray Code, MathWorld.

Example

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;

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

Crossrefs

Cf. A143213.

Sequence in context: A338878 A073166 A050169 * A300380 A300682 A300605

Adjacent sequences: A143211 A143212 A143213 * A143215 A143216 A143217

Keyword

nonn,tabl

Author

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

Extensions

Edited by Michel Marcus and Joerg Arndt, Apr 22 2013

Edited by G. C. Greubel, Aug 27 2024

Status

approved