cp's OEIS Frontend

A385185 Number of permutations of 0..n-1 which are binary Gray codes.

%I A385185 #47 Aug 11 2025 23:11:42
%S A385185 1,2,2,8,4,16,24,144,36,164,192,1168,976,5688,10656,91392,11424,67032,
%T A385185 61840,403568,258956,1589080,2520324,22646880,10898976,67039504,
%U A385185 93326800,819193248,924489888,7399407552,16309883520,187499658240,11718728640
%N A385185 Number of permutations of 0..n-1 which are binary Gray codes.
%C A385185 In a binary Gray code, the binary expansions of any two consecutive terms differ at a single bit position.
%C A385185 When n is odd, the binary weights of n and the first term in the permutation must have opposite parity, since otherwise it's not possible to step through all of 0,...,n-1.
%F A385185 a(2^n) = A091299(n).
%F A385185 a(2^n+1) = a(2^n)/2^(n-1) for n > 0. - _Andrew Howroyd_, Aug 04 2025
%e A385185 For n=5, the a(5) = 4 possible permutations which are Gray codes are
%e A385185   1 3 2 0 4
%e A385185   2 3 1 0 4
%e A385185   4 0 1 3 2
%e A385185   4 0 2 3 1
%e A385185 For n=8, a(8) = 144 includes 0 1 3 2 6 4 5 7 which is lexicographically smallest, and also includes the binary reflected Graycode 0 1 3 2 6 7 5 4.
%o A385185 (MATLAB)
%o A385185 function N = Gcode(L); H = hmap; N = 0; unused = uint8([0: L-1]); for i = 1:length(unused); g = unused(i); u = unused; u(i) = []; gray(g, u); end
%o A385185 function gray(g, u); curidx = g(end) + 1; d = H(curidx,:); if isscalar(u); if d(u+1); N = N + 1; end; else for j = 1: length(u); r = u(j); if d(r+1); nextg = [g r]; nextu = u; nextu(j) = []; gray(nextg, nextu); end; end; end; end
%o A385185 function map = hmap; map = false(L, L); S = uint8([0:L-1]); [X,Y] = meshgrid(S); X = X(:); Y = Y(:);
%o A385185 xb = de2bi(X); yb = de2bi(Y); for k = 1:L^2; v = sum(bitxor(xb(k,:), yb(k,:))); if v == 1; map(k) = true; end; end; end; end
%Y A385185 Cf. A091299, A350784 (when beginning with 0).
%K A385185 nonn,more
%O A385185 1,2
%A A385185 _Ross Drewe_, Aug 03 2025
%E A385185 a(27)-a(33) from _Andrew Howroyd_, Aug 04 2025