These two sequences of positive integers are defined as:
:::: <big><math>\begin{align}
R(1)&=1\ ;\ S(1)=2 \\
R(n)&=R(n-1)+S(n-1), \quad n>1.
\end{align}</math></big>

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The sequence <big><math>S(n)</math></big> is further defined as the sequence of positive integers '''''not''''' present in <big><math>R(n)</math></big>.

Sequence <big><math>R</math></big> starts:
    1, 3, 7, 12, 18, ...
Sequence <big><math>S</math></big> starts:
    2, 4, 5, 6, 8, ...


;Task:
# Create two functions named '''ffr''' and '''ffs''' that when given '''n''' return '''R(n)''' or '''S(n)''' respectively.<br>(Note that R(1) = 1 and S(1) = 2 to avoid off-by-one errors).
# No maximum value for '''n''' should be assumed.
# Calculate and show that the first ten values of '''R''' are:<br> 1, 3, 7, 12, 18, 26, 35, 45, 56, and 69
# Calculate and show that the first 40 values of '''ffr''' plus the first 960 values of '''ffs''' include all the integers from 1 to 1000 exactly once.


;References:
* Sloane's [http://oeis.org/A005228 A005228] and [http://oeis.org/A030124 A030124].
* [http://mathworld.wolfram.com/HofstadterFigure-FigureSequence.html Wolfram MathWorld]
* Wikipedia: [[wp:Hofstadter_sequence#Hofstadter_Figure-Figure_sequences|Hofstadter Figure-Figure sequences]].
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