 | ECS #147 |
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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( Z \right) ,C={\rm Sequence} \left( Z,1
\leq {\rm card} \right) ,E={\rm Prod} \left( B,C \right) ,S={\rm
Sequence} \left( E \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) -3\,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( 1-3\,{\rm \_Z}+{{\rm \_Z}}^{2}
\right) }-1/5\, \left( 3\,\alpha-2 \right) {\alpha}^{-1-n}+
\cases{1&$n=0$\cr 0&otherwise\cr}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {1-2\,x+{x}^{2}}{1-3\,x+{x}^{2}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).