From the conclusion that two people, three people, four people, five people and six people are seated in the right place, it is not difficult to find the recurrence formula of this kind of seating problem. Let n people sit in different places and have a method, then the sequence corresponding to the number of different people sitting is {an. Yizhi a 1=0, a2= 1.

The incorrect seating way of N-ball is an = (n-1) (an-2+an-1) (n ≥ 3). The recurrence formula is as follows: a 1=0, a2= 1, an = (n-1) (an-2+an-1), n≥3, from a 1=0, a2 =

Extended data:

By analogy with the concept of first-order recursive sequence, we might as well define the recursive formula including an+2, an+ 1 and an as second-order sequence, but it is obviously more difficult to find the general term formula with this sequence. In order to facilitate deformation, we can first explain the simple form of the second-order sequence like this [4]:

an+2？ = A * an+ 1？ +B * an？ (Similarly, constant coefficients of A and B)

The basic idea is similar to that of the first order, but we should pay attention to the undetermined coefficients and corresponding terms when compounding.

Original composition: the original shape is transformed into this shape an+2? - ψ * an+ 1？ = ω (an+ 1？ - ψ * an)

Comparing this formula with the original formula, we can get

ψ+ω = A and-(ψ * ω) = b.

By solving these two equations, we can get the values of ψ and ω.

Ling bn? = an+ 1？ - ψ*an？ The original formula becomes bn+ 1? = ω *bn？ Geometric series, can you find bn? The general formula bn= f (n),

That is an+ 1? - ψ*an？ = f (n) (where f (n) is a function about n), and this formula just compounds the definition of first-order sequence, that is, it only contains one+1 and one? Two series variables, so as to achieve "order reduction", change "second order" to "first order", and then solve.

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