Male bees come from unfertilized eggs, so they have mothers but no fathers. Females come from fertilized eggs, so they have parents of both sexes. This produces an interesting pattern: The number of males in a given generation equals the number of females in the succeeding generation. And the number of females in a given generation equals the number of females in the succeeding two generations:
|Genealogy of a male bee, beginning with his "mom" at the bottom level of the chart above (which is the second generation going backwards).|
So the total number of bees, male and female, (but not counting siblings) in generation n is the Fibonacci number F(n).
W. Hope-Jones discovered the relationship in 1921; this example is from Thomas Koshy’s “Fibonacci and Lucas Numbers With Applications”, 2001.