 | ECS #98 |
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1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Union} \left( Z,C \right) ,C={\rm Sequence} \left( Z,3
\leq {\rm card} \right) ,S={\rm Sequence} \left( B,1\leq {\rm card}
\right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) -f \left( n+1 \right) +2\,f \left( n+2
\right) -f \left( n+3 \right) =0,f \left( 0 \right) =0,f \left( 1
\right) =1,f \left( 2 \right) =1,f \left( 3 \right) =2 \right\}
other formats
3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+2\,{\rm \_Z}-{{\rm \_Z}}^{2}+{{
\rm \_Z}}^{3} \right) }1/23\, \left( 1+6\,\alpha+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 {x \left( 1-x+{x}^{2} \right) }{-1+2\,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).