A356658 - OEIS

%I #9 Sep 11 2022 09:30:28

%S 2,8,48,2304,4024320

%N The number of orderings of the hypercube Q_n whose disorder number is equal to the disorder number of Q_n.

%C A proof of a closed form for this sequence will settle Question 3.3 of the preprint "The disorder number of a graph" (see links).

%H M. Dominus, <a href="https://math.stackexchange.com/questions/315544/anti-gray-codes-that-maximize-the-number-of-bits-that-change-at-each-step">"Anti-Gray" codes that maximize the number of bits that change at each step</a>, Mathematics Stack Exchange, 2013.

%H Sela Fried, <a href="https://arxiv.org/abs/2208.03788">The disorder number of a graph</a>, arXiv:2208.03788 [math.CO], 2022.

%e For n = 2, there are exactly two orderings that begin at 00, whose disorder is the disorder number of Q_2, namely, [00, 11, 01, 10] and [00, 11, 10, 01]. Since we can start at any vertex, we need to multiply their number by 2^2, yielding a(2) = 8.

%Y Cf. A271771.

%K nonn,more

%O 1,1

%A _Sela Fried_, Aug 20 2022