A143213 Triangle T(n,m) read by rows: Gray code of A060187(n, k) (decimal representation), 1 <= k <= n, n >= 1.

1, 1, 1, 1, 5, 1, 1, 28, 28, 1, 1, 106, 149, 106, 1, 1, 155, 987, 987, 155, 1, 1, 955, 440, 514, 440, 955, 1, 1, 194, 137, 974, 974, 137, 194, 1, 1, 340, 754, 60, 293, 60, 754, 340, 1, 1, 181, 238, 166, 377, 377, 166, 238, 181, 1, 1, 977, 283, 540, 411, 142, 411, 540, 283, 977, 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,   5,   1;
  1,  28,  28,   1;
  1, 106, 149, 106,   1;
  1, 155, 987, 987, 155,   1;
  1, 955, 440, 514, 440, 955,   1;
  1, 194, 137, 974, 974, 137, 194,   1;
  1, 340, 754,  60, 293,  60, 754, 340,   1;
  1, 181, 238, 166, 377, 377, 166, 238, 181,   1;
  1, 977, 283, 540, 411, 142, 411, 540, 283, 977,  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. A060187, A143214.

Programs

Mathematica

GrayCode[n_, k_]:= FromDigits[BitXor@@@Partition[Prepend[IntegerDigits[n,2,k], 0], 2, 1], 2];
A060187[n_, k_]:= Sum[(-1)^(k-j)*Binomial[n,k-j]*(2*j-1)^(n-1), {j,k}];
A143213[n_, k_]:= GrayCode[A060187[n, k], 10];
Table[A143213[n,k], {n,12}, {k,n}]//Flatten

Formula

T(n, n-k) = T(n, k). - G. C. Greubel, Aug 08 2024

Extensions

Edited by G. C. Greubel, Aug 27 2024