The sequence
1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, ...
The pattern
The sum of the red numbers equals the blue number in the following table
It appears that Mn = Mn-2 + Mn-3 + Mn-4, but is it true?
Let's take a look at what we already know. The population in every month is composed of the following age groups: the newborns, the young, and the adults. (The young are simply the rabbits which are no longer newborns, but not yet mature.) Let An represent the number of newborns in the nth month, let Bn represent the number of young in the nth month, and let Cn represent the number of adults in the nth month.
An = Cn-1, because the number of newborns in this month depends on the number of adults in the previous month.
Bn = An-1, because the number of young in this month depends on the number of newborns in the previous month.
Cn = Cn-1 + Bn-1, because the number of adults in this month depends on the number of adults and the number of young in the previous month.
The pattern
The sum of the red numbers equals the blue number in the following table
It appears that Mn = Mn-2 + Mn-3 + Mn-4, but is it true?Let's take a look at what we already know. The population in every month is composed of the following age groups: the newborns, the young, and the adults. (The young are simply the rabbits which are no longer newborns, but not yet mature.) Let An represent the number of newborns in the nth month, let Bn represent the number of young in the nth month, and let Cn represent the number of adults in the nth month.
An = Cn-1, because the number of newborns in this month depends on the number of adults in the previous month.Bn = An-1, because the number of young in this month depends on the number of newborns in the previous month.
Cn = Cn-1 + Bn-1, because the number of adults in this month depends on the number of adults and the number of young in the previous month.
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