In a genetics study, researchers examined a trait in a population of plants that was controlled by a single gene with two alleles: A (dominant) and a (recessive). They observed that when true-breeding plants with the genotype AA were crossed with true-breeding plants with the genotype aa, all the offspring exhibited the dominant trait. When several of these F1 offspring (Aa) were crossed among themselves, the researchers observed a typical Mendelian phenotypic ratio in the F2 generation. Based on these observations, what phenotypic ratio would they expect to find among the F2 generation?