 | ECS #1075: A simple regular expression |
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1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Prod} \left( {\rm Union} \left( {\rm Sequence} \left( {
\rm Prod} \left( Z,Z \right) \right) ,Z \right) ,{\rm Sequence}
\left( {\rm Union} \left( Z,Z \right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ -2\,f \left( n \right) -f \left( n+1 \right) +f \left( n+2
\right) -1=0,f \left( 0 \right) =1,f \left( 1 \right) =3,f \left( 2
\right) =7,f \left( 3 \right) =14 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{{\rm \_Z}}^{2} \right) }-1/6\,
\left( \alpha+2 \right) {\alpha}^{-1-n}+{\frac {11}{6}}\,{2}^{n}+
\cases{-1/2&$n=0$\cr 0&otherwise\cr}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {-1-x+{x}^{3}}{ \left( -1+{x}^{2} \right) \left( -1+2\,x
\right) }}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).