 | ECS #481: 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( Z,{\rm Union}
\left( Z,{\rm Sequence} \left( Z \right) \right) ,{\rm Sequence}
\left( Z \right) \right) \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) -3\,f \left( n+2 \right) +f \left( n+3
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =1,f \left( 2
\right) =4 \right\}
other formats
3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( 1-3\,{\rm \_Z}+{{\rm \_Z}}^{3}
\right) }-1/9\, \left( -1+2\,{\alpha}^{2}-2\,\alpha \right) {\alpha}^{
-1-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac { \left( -1+x \right) ^{2}}{1-3\,x+{x}^{3}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).