The 2 x n seating derangements

Figures & data

Figure 1. $\mathbf{2}\times \mathbf{4}$ and $\mathbf{2}\times \mathbf{5}$ seating derangements.

Figure 2. $\mathbf{2}\times \mathbf{1}$ seating derangement.

Figure 3. $\mathbf{2}\times \mathbf{2}$ seating derangement.

Figure 4. $\mathbf{2}\times \mathbf{3}$ seating derangement.

Figure 5. Type $\mathit{A}$, type $\mathit{B}$, ..., type $\mathit{M}$.

Figure 6. Type $\mathit{B}$.

Figure 7. Type $\mathit{F}$.

Figure 8. ${\mathit{A}}_{\mathit{n}}$.

Figure 9. ${\mathit{B}}_{\mathit{n}},C_n,D_n,E_n$.

Figure 10. ${\mathit{F}}_{\mathit{n}},G_n,H_n,I_n$.

Figure 11. ${\mathit{J}}_{\mathit{n}},K_n,L_n,M_n$.

Figure 12. 1–1 correspondence between ${\mathit{A}}_{\mathit{n}}\cup B_n\cup D_n\cup F_n\cup H_n$ and $B_{n+\mathbf{1}}$.

Table

n	w(n)	x(n)	y(n)	z(n)	t(n)
1	1	0	0	0	1
2	1	1	0	1	9
3	9	3	2	1	33
4	33	19	10	9	185
5	185	91	58	33	913
6	913	483	298	185	4777
7	4777	2475	1562	913	24,577
8	24,577	12,851	8074	4777	127,385
9	127,385	66,427	41,850	24,577	658,801
10	658,801	343,939	216,554	127,385	3,410,313