 | ECS #468: 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,Z,{\rm Union}
\left( Z,Z \right) ,{\rm Sequence} \left( Z \right) \right) \right)
\right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ 2\,f \left( n \right) +f \left( n+2 \right) -f \left( n+3
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =0,f \left( 2
\right) =0 \right\}
other formats
3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{\rm \_Z}+2\,{{\rm \_Z}}^{3}
\right) }-1/29\, \left( 1+3\,{\alpha}^{2}-10\,\alpha \right) {\alpha}^
{-1-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {-1+x}{-1+x+2\,{x}^{3}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).