 | ECS #164 |
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1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Sequence} \left( E \right) ,C={\rm Prod} \left( Z,B
\right) ,E={\rm Sequence} \left( Z,1\leq {\rm card} \right) ,F={\rm
Sequence} \left( C,1\leq {\rm card} \right) ,S={\rm Sequence} \left( F
\right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ 2\,f \left( n \right) -4\,f \left( n+1 \right) +f \left( n+2
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =1,f \left( 2
\right) =3 \right\}
other formats
3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( 1-4\,{\rm \_Z}+2\,{{\rm \_Z}}^{2}
\right) }1/4\,{\alpha}^{-n}+\cases{1/2&$n=0$\cr 0&otherwise\cr}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {1-3\,x+{x}^{2}}{1-4\,x+2\,{x}^{2}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).