 | ECS #461: 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 Union} \left( {\rm Sequence} \left( {\rm Union} \left(
Z,Z \right) \right) ,{\rm Sequence} \left( {\rm Prod} \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) =2,f \left( 1 \right) =2,f \left( 2
\right) =5 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{{\rm \_Z}}^{2} \right) }1/2\,{
\alpha}^{-n}+{2}^{n}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {-2+{x}^{2}+2\,x}{ \left( -1+2\,x \right) \left( -1+{x}^{2}
\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).