This paper addresses the elementary properties of the Pell sequence a_n, which is defined by the initial terms a₀ = 0, a₁ = 1, and by the recursion a_n+1 = 2a_n + a_n-1. A closed analytical formula for the members of the sequence, established connections with the Pell equation x² - 2y² = ±1, and with primitive Pythagorean triples, are proven. Sums and quotients related to this sequence are studied. All of the results presented are well known, and the problems discussed are exercises at an undergraduate level. On the other hand, the presentation does have some didactic value.