 | ECS #903: A simple regular expression |
| Introduction | Examples | Search | Submit | Help | Links |
1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Sequence} \left( {\rm Prod} \left( {\rm Union} \left( Z
,{\rm Prod} \left( Z,Z,Z \right) \right) ,Z,Z \right) \right)
\right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) +f \left( n+2 \right) -f \left( n+5
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =0,f \left( 2
\right) =0,f \left( 3 \right) =1,f \left( 4 \right) =0 \right\}
other formats
3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{{\rm \_Z}}^{3}+{{\rm \_Z}}^{5}
\right) }{\frac {1}{3233}}\, \left( -60+100\,{\alpha}^{2}+250\,{\alpha
}^{4}+661\,\alpha+36\,{\alpha}^{3} \right) {\alpha}^{-1-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
- \left( -1+{x}^{3}+{x}^{5} \right) ^{-1}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).