MathDB

Define a domino to be an ordered pair of distinct positive integers. A proper sequence of dominoes is a list of distinct dominoes in which the first coordinate of each pair after the first equals the second coordinate of the immediately preceding pair, and in which

(i, j)

and

(j, i)

do not both appear for any

i

and

j

. Let

D_n

be the set of all dominoes whose coordinates are no larger than

n

. Find the length of the longest proper sequence of dominoes that can be formed using the dominoes of

D_n

Problem Statement