A350784 Number of Gray code sequences of length 2*n where numbers are between 0 and 2*n-1.

1, 2, 2, 12, 8, 44, 192, 2688, 1344, 6896, 24228, 316848, 812624, 9158880, 75652512, 1813091520, 725236608, 3568226496, 11152502816, 137997707616, 309878131724

Offset: 1

Author

Thomas König, Jan 16 2022

Keywords

• nonn
• hard
• more

Comments

The sequences are given with the first term as zero.

Examples

			The following Gray codes of length 10 contain only the numbers between 0 and 9:
  0, 2, 3, 7, 6, 4, 5, 1, 9, 8;
  0, 2, 6, 4, 5, 7, 3, 1, 9, 8;
  0, 4, 5, 7, 6, 2, 3, 1, 9, 8;
  0, 4, 6, 2, 3, 7, 5, 1, 9, 8;
  0, 8, 9, 1, 3, 2, 6, 7, 5, 4;
  0, 8, 9, 1, 3, 7, 5, 4, 6, 2;
  0, 8, 9, 1, 5, 4, 6, 7, 3, 2;
  0, 8, 9, 1, 5, 7, 3, 2, 6, 4.
Therefore a(5) = 8.
		

Links

• Thomas König, Fortran program for calculating the sequence
• Wikipedia, Gray code
• Wikipedia, Hamming distance

Crossrefs

Cf. A003042 (a subsequence), A003188, A236602, A290772.

Programs

Fortran

! See König link.

Formula

a(2^m) = A003042(m+1).

a(n) = 2 * A236602(n) for n >= 2. - Alois P. Heinz, Feb 01 2022

Extensions

a(17)-a(18) (via A236602) from Alois P. Heinz, Feb 01 2022

a(19)-a(20) from Martin Ehrenstein, Feb 16 2022

a(21) from Martin Ehrenstein, Feb 21 2022