 | ECS #1019: 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 Prod} \left( {\rm Sequence} \left( {\rm Union} \left( {
\rm Prod} \left( Z,Z \right) ,Z \right) \right) ,{\rm Union} \left( {
\rm Sequence} \left( Z \right) ,Z \right) \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ -f \left( n \right) -f \left( n+1 \right) +f \left( n+2
\right) -1=0,f \left( 0 \right) =1,f \left( 1 \right) =3,f \left( 2
\right) =5 \right\}
other formats
3.3. Closed form
\displaystyle
-1+\sum _{\alpha={\rm RootOf} \left( -1+{{\rm \_Z}}^{2}+{\rm \_Z}
\right) }2/5\, \left( 3+\alpha \right) {\alpha}^{-1-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {-1-x+{x}^{2}}{ \left( -1+{x}^{2}+x \right) \left( -1+x
\right) }}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).