RO-NMO 2008 Problem 82

a) We call admissible sequence a sequence of 4 even digits in which no digits appears more than two times. Find the number of admissible sequences.

b) For each integer $n\geq 2$ we denote $d_n$ the number of possibilities of completing with even digits an array with $n$ rows and 4 columns, such that

(1) any row is an admissible sequence; (2) the sequence 2, 0, 0, 8 appears exactly ones in the array.

Find the values of $n$ for which the number $\frac {d_{n+1}}{d_n}$ is an integer.