 | ECS #880: 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 Prod} \left( {\rm Sequence} \left( Z \right) ,{\rm
Sequence} \left( {\rm Prod} \left( {\rm Union} \left( Z,Z \right) ,Z,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+3 \right) -1=0,f \left( 0
\right) =1,f \left( 1 \right) =1,f \left( 2 \right) =1 \right\}
other formats
3.3. Closed form
\displaystyle
-1+\sum _{\alpha={\rm RootOf} \left( -1+2\,{{\rm \_Z}}^{3} \right) }1/3
\, \left( 2\,{\alpha}^{2}+2\,\alpha+1 \right) {\alpha}^{-1-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {1}{ \left( -1+x \right) \left( -1+2\,{x}^{3} \right) }}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).