 | ECS #447 |
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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 Union} \left( Z,{\rm Sequence}
\left( Z \right) \right) ,{\rm Sequence} \left( {\rm Prod} \left( Z,Z
,Z \right) \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) -n-4=0,f \left( 0 \right) =1,f \left( 1 \right) =2,f \left( 2
\right) =1 \right\}
other formats
3.3. Closed form
\displaystyle
1+\sum _{\alpha={\rm RootOf} \left( {{\rm \_Z}}^{2}+{\rm \_Z}+1
\right) }-2/9\, \left( \alpha+2 \right) {\alpha}^{-n-1}+1/3\,n
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {-x+{x}^{2}-1}{ \left( -1+x \right) \left( -1+{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).