Rabbits
Phyllotaxis: Pine cones and their spirals
Spirals of squares
Tilings of rectangles
fn is
- the number of sequences with 1's and 2' such that the sum is n-1
- the number of possible sequences of single houses and double houses
in a street with n-1 houses.
- the number of tilings of the 2×(n-1) rectangle using
dominoes.
Proof, using the recurrence formula: the sequence may start with 1,
there are fn-1 possibilities, or with 2, there are
fn-2 possibilities. For n = 1 and n = 2, the number is 1.
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