WE GIVE A NEW CHARACTERIZATION OF GENERALIZED BÜCHI SEQUENCES (SEQUENCES WHOSE SEQUENCE OF SQUARES HAS CONSTANT SECOND DIFFERENCE (A), FOR SOME FIXED INTEGER A) OF LENGTH 3 OVER THE INTEGERS AND A STRATEGY FOR ATTACKING BÜCHIS N SQUARES PROBLEM. KNOWN CHARACTERIZATIONS OF INTEGER BÜCHI SEQUENCES OF LENGTH 3 ARE ACTUALLY CHARACTERIZATIONS OVER THE RATIONALS, PLUS SOME DIVISIBILITY CRITERIONS THAT KEEP INTEGER SEQUENCES.