MathDB

Let

\mathbb{A}

be the least subset of finite sequences of nonnegative integers that satisfies the following two properties:
-

(0,0) \in \mathbb{A}

- If

(a_1,\ldots,a_n)\in \mathbb{A}

then

(a_1,\ldots,a_{i-2},a_{i-1}+1,1,a_{i}+1,a_{i+1},\ldots,a_n)\in \mathbb{A}

for all

i\in \{2,\ldots,n\}

.
For each

n\geq 2

, let

\mathbb{B}(n)

be the set of sequences in

\mathbb{A}

with

n

terms. Find the number of elements of

\mathbb{B}

Problem Statement