 | ECS #401 |
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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 Prod} \left( Z,{\rm Sequence}
\left( Z \right) ,{\rm Union} \left( Z,{\rm Prod} \left( Z,Z \right)
\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) -f \left( n+3 \right) =0,f \left( 0 \right) =1,f \left( 1
\right) =0,f \left( 2 \right) =1 \right\}
other formats
3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{\rm \_Z}+{{\rm \_Z}}^{2}+{{\rm
\_Z}}^{3} \right) }-1/22\, \left( -1-6\,\alpha+3\,{\alpha}^{2} \right)
{\alpha}^{-1-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {-1+x}{-1+x+{x}^{2}+{x}^{3}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).