 | ECS #933: 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 Union} \left( Z,{\rm Prod}
\left( {\rm Union} \left( Z,Z \right) ,Z,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) -f \left( n+4
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =1,f \left( 2
\right) =1,f \left( 3 \right) =1 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{\rm \_Z}+2\,{{\rm \_Z}}^{4}
\right) }{\frac {1}{539}}\, \left( 27+72\,{\alpha}^{3}+96\,{\alpha}^{2
}+128\,\alpha \right) {\alpha}^{-1-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
- \left( -1+x+2\,{x}^{4} \right) ^{-1}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).