 | ECS #460: 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 Sequence} \left( {\rm Prod} \left( {\rm Union} \left( Z
,Z \right) ,{\rm Sequence} \left( Z \right) ,{\rm Sequence} \left( Z
\right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) -4\,f \left( n+1 \right) +f \left( n+2
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =2,f \left( 2
\right) =8 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( 1-4\,{\rm \_Z}+{{\rm \_Z}}^{2}
\right) }-1/3\, \left( 2\,\alpha-1 \right) {\alpha}^{-1-n}+
\cases{1&$n=0$\cr 0&otherwise\cr}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac { \left( -1+x \right) ^{2}}{1-4\,x+{x}^{2}}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).