|
%I #39 Feb 28 2022 07:38:47
%S 1,2,2,12,8,44,192,2688,1344,6896,24228,316848,812624,9158880,
%T 75652512,1813091520,725236608,3568226496,11152502816,137997707616,
%U 309878131724
%N Number of Gray code sequences of length 2*n where numbers are between 0 and 2*n-1.
%C The sequences are given with the first term as zero.
%H Thomas König, <a href="/A350784/a350784_1.f90.txt">Fortran program for calculating the sequence</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gray_code">Gray code</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamming_distance">Hamming distance</a>
%F a(2^m) = A003042(m+1).
%F a(n) = 2 * A236602(n) for n >= 2. - _Alois P. Heinz_, Feb 01 2022
%e The following Gray codes of length 10 contain only the numbers between 0 and 9:
%e 0, 2, 3, 7, 6, 4, 5, 1, 9, 8;
%e 0, 2, 6, 4, 5, 7, 3, 1, 9, 8;
%e 0, 4, 5, 7, 6, 2, 3, 1, 9, 8;
%e 0, 4, 6, 2, 3, 7, 5, 1, 9, 8;
%e 0, 8, 9, 1, 3, 2, 6, 7, 5, 4;
%e 0, 8, 9, 1, 3, 7, 5, 4, 6, 2;
%e 0, 8, 9, 1, 5, 4, 6, 7, 3, 2;
%e 0, 8, 9, 1, 5, 7, 3, 2, 6, 4.
%e Therefore a(5) = 8.
%o (Fortran) See link.
%Y Cf. A003042 (a subsequence), A003188, A236602, A290772.
%K nonn,hard,more
%O 1,2
%A _Thomas König_, Jan 16 2022
%E a(17)-a(18) (via A236602) from _Alois P. Heinz_, Feb 01 2022
%E a(19)-a(20) from _Martin Ehrenstein_, Feb 16 2022
%E a(21) from _Martin Ehrenstein_, Feb 21 2022
|
