1 . We consider binary $2 \times n$ matrices, i.e., matrices with 2 rows and $n$ columns, in which each entry is 0 or 1. A column in such a matrix is called a $1 \atop 1$-column, if both bits in the column are 1.
For any integer $n \geq 1$ and integer $k$ with $0 \leq k \leq n$, let $M(n,k)$ be the number of binary $2 \times n$ matrices

• that do not contain any $1 \atop 1$-column, and
• contain exactly $k$ many 1's.

Which of the following is true for all integers $n \geq 2$ and $k$ with $1 \leq k \leq n-1$?