 | ECS #1054: 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
,Z,Z \right) ,{\rm Union} \left( {\rm Sequence} \left( Z \right) ,Z
\right) \right) \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ 3\,f \left( n \right) -3\,f \left( n+1 \right) -4\,f \left( n+
2 \right) +f \left( n+3 \right) =0,f \left( 0 \right) =1,f \left( 1
\right) =3,f \left( 2 \right) =15 \right\}
other formats
3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( 1-4\,{\rm \_Z}-3\,{{\rm \_Z}}^{2}+3\,
{{\rm \_Z}}^{3} \right) }-{\frac {1}{95}}\, \left( -11-22\,\alpha+15\,{
\alpha}^{2} \right) {\alpha}^{-1-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {-1+x}{1-4\,x-3\,{x}^{2}+3\,{x}^{3}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).