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The Fibonacci(n, a, b) generates the nth Fibonacci string, with initial values a and b. The arguments after the first are optional, and default to the strings $''0''$ and $''1''$, respectively.

Given starting symbols a and b, the nth Fibonacci string is defined by the recurrence Fibonacci( n, a, b ) = cat( Fibonacci( n - 1, a, b ), Fibonacci( n - 2, a, b ) ), for $1<n$, and the initial conditions Fibonacci( 0, a, b ) = b and Fibonacci( 1, a, b ) = a. The length of Fibonacci( n ) is equal to the nth+1 Fibonacci number.

The Fibonacci procedure has option remember.

All of the StringTools package commands treat strings as (null-terminated) sequences of $8$-bit (ASCII) characters. Thus, there is no support for multibyte character encodings, such as unicode encodings.

$\mathrm{with}\left(\mathrm{StringTools}\right)\&colon;$

$\mathrm{Fibonacci}\left(5\right)$

$''01001010''$

$\mathrm{Fibonacci}\left(5\&comma;''u''\&comma;''v''\right)$

$''uvuuvuvu''$

$\mathrm{seq}\left(\mathrm{length}\left(\mathrm{Fibonacci}\left(i\right)\right)\&comma;i=1..10\right)$

$1,2,3,5,8,13,21,34,55,89$

$\mathrm{seq}\left(\mathrm{combinat}\left['\mathrm{fibonacci}'\right]\left(1+i\right)\&comma;i=1..10\right)$

$1,2,3,5,8,13,21,34,55,89$