 | ECS #910: 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( Z \right) ,{\rm
Sequence} \left( {\rm Prod} \left( {\rm Sequence} \left( Z \right) ,{
\rm Sequence} \left( Z \right) ,Z \right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ -f \left( n \right) +3\,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) =4,f \left( 3 \right) =9 \right\}
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3.3. Closed form
\displaystyle
1+\sum _{\alpha={\rm RootOf} \left( 1-3\,{\rm \_Z}+{{\rm \_Z}}^{2}
\right) }-1/5\, \left( 3\,\alpha-2 \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 {-2+6\,x-4\,{x}^{2}+{x}^{3}}{ \left( -1+x \right) \left( 1-3\,x
+{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).