A356658 The number of orderings of the hypercube Q_n whose disorder number is equal to the disorder number of Q_n.

2, 8, 48, 2304, 4024320

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..5.

M. Dominus, "Anti-Gray" codes that maximize the number of bits that change at each step, Mathematics Stack Exchange, 2013.

Sela Fried, The disorder number of a graph, arXiv:2208.03788 [math.CO], 2022.

Example

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.

Crossrefs

Cf. A271771.

Sequence in context: A322309 A009745 A009751 * A279239 A279109 A355667

Adjacent sequences: A356655 A356656 A356657 * A356659 A356660 A356661

Keyword

nonn,more

Author

Sela Fried, Aug 20 2022

Status

approved